Google This is a digital copy of a book that was preserved for generations on Hbrary shelves before it was carefully scanned by Google as part of a project to make the world's books discoverable online. It has survived long enough for the copyright to expire and the book to enter the public domain. A public domain book is one that was never subject to copyright or whose legal copyright term has expired. Whether a book is in the public domain may vary country to country. Public domain books are our gateways to the past, representing a wealth of history, culture and knowledge that's often difficult to discover. Marks, notations and other maiginalia present in the original volume will appear in this file - a reminder of this book's long journey from the publisher to a library and finally to you. Usage guidelines Google is proud to partner with libraries to digitize public domain materials and make them widely accessible. Public domain books belong to the public and we are merely their custodians. Nevertheless, this work is expensive, so in order to keep providing this resource, we liave taken steps to prevent abuse by commercial parties, including placing technical restrictions on automated querying. We also ask that you: + Make non-commercial use of the files We designed Google Book Search for use by individuals, and we request that you use these files for personal, non-commercial purposes. + Refrain fivm automated querying Do not send automated queries of any sort to Google's system: If you are conducting research on machine translation, optical character recognition or other areas where access to a large amount of text is helpful, please contact us. We encourage the use of public domain materials for these purposes and may be able to help. + Maintain attributionTht GoogXt "watermark" you see on each file is essential for informing people about this project and helping them find additional materials through Google Book Search. Please do not remove it. + Keep it legal Whatever your use, remember that you are responsible for ensuring that what you are doing is legal. Do not assume that just because we believe a book is in the public domain for users in the United States, that the work is also in the public domain for users in other countries. Whether a book is still in copyright varies from country to country, and we can't offer guidance on whether any specific use of any specific book is allowed. Please do not assume that a book's appearance in Google Book Search means it can be used in any manner anywhere in the world. Copyright infringement liabili^ can be quite severe. About Google Book Search Google's mission is to organize the world's information and to make it universally accessible and useful. Google Book Search helps readers discover the world's books while helping authors and publishers reach new audiences. You can search through the full text of this book on the web at |http : //books . google . com/| \ I • il I. 712322 - I I ^^€ 7 « • UNITED STATES GEOLOGICAL SURVEY J. W. POWttLL, UIRECTOB oc ON THE THEMO-ELECTllIC/ MEASUREMENT HIGH TEMPERATURES OA.RL BARU8 %-^, WASHINGTON GOVERNMENT PRINTING OFHTCB 1889 CONTENTS. Page. Letter of transmittal ir> Preface 17 Introdactioii 23 General accoant of methods of pyrometry 23 Earlier digests 23 Character of the measarcments 24 Classification of pyrometers 25 Dilatation of solids 25 Dilatation of liquids 27 Dilatation of gases (manometric methods) 27 Dilatation o^ gases (displacement methodH) 3G Vapor tension 38 Dissociation 38 Fusion 39 Specific heat 40 Ebullition 42 Heat conduction 42 Radiation 43 Viscosity 46 Acoustics 47 Thermo-electrics .: 48 Electrical conductivity 50 liagnetism 52 Interpolation methods 52 Advantages of thermo-electric pyrometry 52 Chapter I. — ^llie degree of constant high temperature attained in iii<>tal1io vapor baths of large dimensions ; by C. Barus and W . Hallock r>(> Explanation 5() Apparatus 57 Remarks 57 Low boiling points 58 Boiling points between 100^ and 300° 59 Apparatus for mercury (51 Boiling point of zinc 02 Experimental results C7 Methods of measurement 67 List of thermo-couples 68 Data for mercury vapor baths 69 Data for zinc vapor baths - 70 Inferences relative to low percentage alloys 77 Reduction of data 77 Series of alloys... 79 (659) 5 CONTENTS. Chapter II. — The calibration of electrical pyrometers by the aid of fixed thermal data 84 Explanation 84 Apparatus for low boiling points (100° to 500°) 84 Original forms of boiling tubes 84 Perfected forms of boiling tubes 86 Boiling-point tubes for pressure work '. 88 Dr. Gibbs'sring burner 90 Apparatus for high boiling points 90 Original forms of boiling-poiut crucible 90 Perfected forms of boiling>point crucible 91 Insulators 95 Method of measurement 97 Thermo-element 97 Standards of electromotive force 99 Method of computation 103 Experimental results 104 Exploration for constancy of temperature; water, aniline 104 Exploration for constancy of temperature, mercury 105 Exploration for constancy of temperature, sulphur 107 Exploration for constancy of temperature, zinc 108 Practical calibration 110 Investigation of data 110 Discussion of data 114 Time-variation of thermo-electric data 116 Duration of continued ebullition, constant high temperature 116 Duration of continued ebullition, constant low temperature 116 Available substances for boiling points 119 Points of volatiliEation 121 Subsidiary' (lata : antimony ; bismuth ; cadmium 122 Thermo-electric datum for the melting point of platinum 124 Chapter III. —Certain pyro-electric properties of the alloys of platinum 126 P^xplanation .• 126 Fusion and mechanical treatment of the alloys 128 Fusion and rolling 12H Preliminary data, density 128 Preliminary data, electrical resistance of rods 131 Experimental data -. VXi Further mechanical treatment ; resistance of wires VX^ Thermo-electrics of wires i:^ Temperature coefficient ^ i;i9 Qeneral digest 143 Discussion and inferences 144 Earlier results 144 Resistance and density 145 Resistance and thermo-electrics 146 Electrical t^^sts for purity 146 Electrical resistance and temperature coefficient 149 Other relevant results 157 General remarks 161 Chapter IV. — The calibration of electrical pyrometers by direct comparison with the air thermometer 165 Displacement methods of thermometry 1()5 Constant volume thermometers 167 (060) CONTENTS. 7 Page. Chapter IV — Continned. ManomctiT ICT Metallic capillary tubes .' 169 Porcelain air-thermometer bulbs 171 Machine for aoldering porcelain 175 Revolving muffle 180 Remarks regarding apparatus and manipulation 185 Constant volume air thormometer — method of computation 188 The general equation 188 The equation simplified 190 Errors of the approximations 190 Compensator 192 Errors of measurement in general 195 Constant volume air thermometer — experimental results 198 Earlier results 198 Later results 204 Digression 20C Const-ant pressure air thermometry — apparatus 208 Constant pressure air thermometry — method of computation 210 The general equation 210 The equation simplified 211 Volumetry of bulbs 213 Errors of the approximations 214 Compensator 21-5 Constant pressure air thermometer — experimental results 2l(> Manipulation 210 Experimental data 217 Graphic digests 227 Constant pressure air thermometer — discussion 227 Errors of measurement, in general 227 Accuracy of the measurements made, group I 231 Accuracy of the measurements made, group II 21^2 Boiling point of zinc ' 233 Coefticient of heat expansion of porcelain 230 Remarks 237 Chaptkr V. — The pyrometric use of the principle of viscosity ^ 239 Introduction 239 Remarks 2:}9 Literature 240 Transpiration subject to the Poiseuille-Meyer law 242 Apparatus 242 General disposition of parts 242 Apparatus for constant pressure 244 The capillary apparatus 245 Differential a])paratus 249 Method of heating 249 Methods of computation 251 The general equation 1 251 Ca8<» of t wo cold ends, absolute apparatus 252 Case of two cold ends, differential apparatus 254 Experimental results 255 Manipulation 255 Nomenclature 256 Data 258 (061) 8 CONTENTS. Chapter V— Continued. Discussion 271 Viscosity at zero 271 Viscosity at high temperatures, kinetic inferences 273 Sources of error 274 Diffusion 275 Sliding coefficient 276 Advantages of an exponential law 277 Effect of imperfect gaseity 279 Tlie new method of pyronietry 281 Methods of computation 281 Results 282 Transpiration not subject to the Poisouille-Meyer law 284 Objects of the investigation 284 Hoffmann's researches 285 Experimental results 2H7 Transpiration under variable pressure 287 Transpiration nnder constant pressure 288 Transpirations compared differentially 293 Discussion 295 Apparent viscosity and pressure 295 Apparent viscosity and temperature 297 Obliquity of the linear loci 297 Supplementary results 298 General remarks 300 The new method of pyrometry ". 302 Practical remarks 302 Appurtenances 302 The transpiration pyrometer 302 (662) ILLUSTRATIONS. Pug©. Fig. 1. Apparatus for constant temperature between (P and 100^ 59 2. Apparatus for constant temperatare between 100^ and 300^ 60 3. Boiling-point apparatus for mercnry 61 4. Boiling-point apparatus for zinc ; earlier form 63 5. Boiling-point apparatus for zinc ; later form ; longitudinal section. .. 65 6. Boiling-point apparatus for zinc ; later form ; cross-section 66 7. Boiling-point tube for mercury ; original form ' 84 8. Boiling-point tube for sulphur ; original form 85 9. Boiling-point tube for water, etc. ; original form 86 10. Boiling-point tube ; perfected form 87 10a. Boiling-point tube for annealing long wires 87 11. Boiling-point tube for pressure work 88 11a. Boiling-point tube for pressure work with accessories 88 12. Ring burner 89 13. Original form of boiling-point crucible 91 14. Perfected form of boiling-point crucible 92 14a. Boiling-point crucible for pressure work > 94 15. Boiling-point xsrucible with open tube 94 16. Machine for pressing porcelain insulators 96 17. Die for porcelain tubes 96 18. Disposition of thermo-electric apparatus ...•• 97 19. Double key 97 20. Standard Daniell cell 100 21. Chart showing the relation of temperature and electromotive force ; thermo-couples NoH. 17 and 18 114 22. Chart showing the relation of temperature and electromotive force ; thermo-couples Nos. 22, 35, 36, 37, 38, 39, 40 116 23. Apparatus for melting point of platinum 124 24. Resistometer 132 25. Detached rider .' 132 26. Chart showing the relation between electrical resistance and tempera- ture coefficient of platinum alloys 150 27. Chart showing the relation between electrical conductivity and tem- perature coefficient of platinum alloys 162 28. Tubular displacement air thermometer 166 29. (Withdrawn.) 30. Diagram of Jolly air thermometer and bulb 1G8 31. Non-iuglazed, spherical air-thermomoter bulb 172 32. Non-inglazed, re-entrant air-thermometer bulb 173 33. Inglazed, spherical air- thermometer bulb 174 34. Machine for soldering porcelain ; elevation 175 35. Machine for soldering porcelain ; plan 176 35a. Gasometers 179 (663) 9 10 ILLUSTRATIONS. Fig. '*5€). Revolving muffle ; diagram 181 3Ga. Elliptic revolviDg muffle ; diagram 181 37. Revolving muffle and furnace ; longitudinal section 182 38. Revolving muffle and furnace; plan 184 39. Temperature and electromotive force of thermo-coupleH, in correspond- ing time series 202 40. Constant pressure air thermometer 209 41. Chart showing the variation of thenuo-electromotive force with tem- perature 226 42. Chart showing the variation c»f thermo-electromotivo force with tem- perature 228 43. General disposition of apparatus for viscosity measurement 243 44. Diagram of receiver for distributing pressure 246 45. Side elevation of the capillary apparatus 247 46. Plan of the capillary apparatus 248 47. Vertical section through helix 2i>8 47a. Plan of helix and thermo-couples 2(k1 48. Chart showing viscosity as a function of tem]>eratnre 264 49. 50. 51. ^ Diagrams of practical transpiration pyrometers 303 5'- '«'• 54. Chart showing the relation between apparent viscoHi ry ]iud pressure . . 'M)A 55. Disposition of apparatuH for diflVrential ineaHuremonts IW5 (CG4) • TABLES. \ Page. Tablr 1. List of thermo-con plea 69 2. Constancy of temperature in the mercnry apparatus 70 3. Constancy of temperature in the zinc apparatus 72 4. Constancy of temperature ; zinc apparatus ; time series 73 5. Constancy of temperature ; zi nc apparatus ; time series 74 6. Values of eW 78 7. General summary of results 79 8. Equivalent thermo-electromotive forces 80 9. Comparison of standard elements 101 10. Temperature coefficient of Clark's cells 102 11. Temperature coefficient of siphon Daniell standard 102 12. Constancy of temperature along the axis of boiling tube ; steam.. . 10r> 13. Constancy of temperature along the axis of boiling tube ; mercury. 1(H) I4ji Constancy of temperature along the axis of boiling tube; sulphur. 107 15. Constancy of temperature along the axis of boiling crucible ; zinc. . 109 16. Calibration ofthermo-couplesNos. 17, 18,22,35,36 110 17. Values of 6:20 for thermo-couples Nos. 17, 18, 22, 35, 36 114 18. Crucible (fig. 13) charged with bismuth.*. 117 19. Crucible (fig. 13) charged with antimony 117 20. Crucible (fig. 13) charged with cadmium 118 21. Constancy of temperature in boiling tubes; sulphur 119 22. Available substances for vapor baths 120 23. Calibration in zinc vapor 122 24. Calibration in zinc vapor 12:5 25. Calibration in hot tin 123 26. Calibration in bismuth 123 27. Calibration in antimony 124 28. Thermo-electric datum for temperatures above the melting point of platinum 125 29. Density of platinum alloys 129 30. Electrical resistance of platinum alloys; rods 132 31. Electrical resistance of platinum alloys; wires • 134 32. Thermo-electrics of platinum alloys 136 3.3. Temperature coefficient of platinum alloys 139 34. Constants of platinum alloys; digest 143 35. Electrical tests for purity 147 36. Electrical test^ for purity 147 37. Electrical tests for purity 147 38. Electrical tests for purity 148 39. Electrical tests for purity 14H 40. Constants of the linear relation (initial tangent) between electrical conductivity and temperature coefficient of platinum alloys 155 (665) ' 11 12 TABLES. Table 40a. Showing Matthleasen's and Vogt's resolts for the eleotrloB of gold, silver, and copper alloys 158 40h. Showing Matthiessen's and Vogt's results for iron carburets 160 41. Dimensions of copper capillary tubes 171 42. Dimensions of platinum capillary tubes 171 43. Capacity, etc., of porcelain air-thermometer bulbs 173 44. Values of ifcfordiversT 191 45. Values of H-Jf for divers T and « 192 46. Compensator Yolumetry 194 47. Comparison of divers errors which affect the result one promille.. 196 48. Moisture error of unglazed bulbs 198 49. Moisture error of unglazed bulbs 199 50. Comparison of ilir thermometer and thermo-couple 200 51. Comparison of air thermometer and thermo-couple 202 52. Comparison of air thermometer and thermo-couple ; later results.. 204 53. Comparison of 090 and T from Table 52 206 54. Comparison of air thermometer and thermo-couple ; in-glazed bulb. 207 55. Comparison of 020 and T from Table 54 308 56. Volumetry of bulbs 213 57. Errors of the thermometer formulffi 215 58. Comparison of air thermometer and thermo-couple ; method con- stant pressure ; time series ; Group I, Series 1 218 59. Comparison of air thermometer and thermo-couple ; method con- stant pressure ; time series; Group I, Series II 218 60. Comparison of air thermometer and thermo-couple ; method con- stant pressure ; time series ; Group I, Series III 219 61. Comparison of air thermometer and thermo-couple ; method con- stant pressure ; time series ; Group I, Series IV 220 62. Comparison of air thermometer and thermo-couple ; method con- stant pressure ; time series ; Group II, Series 1 221 63. Comparison of air thermometer and thermo-couple ; method con- stant pressure; time series; Group II, Series II 222 64. Comparison of air thermometer and thermo-couple ; method con- stant pressure ; time series ; Group II, Series III 222 65. Comparison of air thermometer and thermo-couple ; method con- stant pressure ; time series; Group II, Series IV 223 66. Comparison of air thermometer and thermo-couple ; method con- stant pressure ; time series ; Group II, Series V 223 67. fao and T from Table 58 224 68. eao and T from Table 59 225 69. e«o and T from Table 60 225 70. «ao and T from Table 61 225 71. flao and T from Table 62 225 72. 020 and T from Table 63 226 73. 020 and T from Table 64 226 74. 020 and T from Table 65 226 75. e«, and T from Table 66 227 76. Comparison of divers errors which affect the result one promille .. 229 77. Permanent volume variations of bulb 233 78. Interpolations near the boiling point of zinc 235 79. Coefficient of heat expansion of porcelain 236 80. Thermal constants of the petroleum argand lamp 250 81. Viscosity of air. 259 82. Viscosity of hydrogen 260 (666) TABLES. 18 83. Yisoosity of hydrogen 262 84. Viscosity of air 263 ^. Viscosity of air, miBoellaneons tests 265 86. Viscosity of air, misceUaneons tests 267 87. Viscosity of hydrogen 268 88. Viscosity of hydrogen 2G9 89. Viscosity of air 269 90. Saccessive value of 970 271 91. Calculated zero valnes of — • 278 92. Temperatures measured thermo-eleotrioally and hy the transpira- tion pyrometer 283 93. Transpiration of air under variable pressure, burner not chimneyed . 287 94. Transpiration of -air under variable pressure, chimneyed burner. . . 288 95. Transpiration of air under variable pressure 288 96. Apparent viscosity of air at high temperatures ; absolute measure- ment 290 97. Apparent viscosity of air at high temperatures ; absolute measure- ment 290 98. Apparent viscosity of air at high temperatures; absolute measure- ment 291 99. Apparent viscosity of air at high temperatures; absolute measure- ment .* 291 100. Apparent viscosity of air at high temperatures ; absolute measure- ment 292 101. Apparent viscosity of air at high temperatures; differential measurement 294 102. Apparent viscosity of air at high temperatures; differential measurement 294 103. Apparent viscosity of air at high temperatures; differential measurement 294 104. Transpiration and pressure in wide tubes 297 106. Transpiration and. pressure in glass tubes • 298 106. Transpiration and pressure in silver tubes 299 107. Transpiration and pressure in platinum tubes, air 299 108. Transpiration and pressure in platinum tubes, hydrogen 300 (667) LETTER OF TRANSMITTAL. Department of the Interiob, United States Geological Survey, Division of Chemistry, Washingf^m, D. C, February 20, 1888. Sir: I have the honor to transmit herewith the manuscript ^of Dr. Carl Barus's report "(Jn the Thermo-electric Measurement of High Temperatures,'' and to request that it be published as a bulletin of the U. S. Geological Survey. Very resi)ectfully, F. W. Clarke, Chief Chemist, Hon. J. VV. Powell, Director U. ti. Geological Survey. (669) 15 PREFACE. The present publicatiou is tbe first contribution to a research on the physical constants of rocks, the experiments of which are to follow a general plan devised by Mr. Clarence King, former Director of the U. S. Geological Survey. Retaining such questions as have an imme- diate bearing on dynamical geology for his own investigation, Mr. King honore, p. 40. ^Of, First Ann. Rept. U. S. Geol. Survey, IddO, p. 4«i; Second Ann. Rep t. U. S. Geol. Survey, 1h82, pp. 3U, 319-3.30. » Third Ann. Rcpt. U. S. Geol. Survey, 18^3, pp. :V-9. Pull, 54 2 "(071) 17 18 MEASUREMENT OF HIGH TEMPERATURES. (fc) Plienomoua of elasticity and viscoaity, considered, an before, with especial refer- ence to their dependence on temperature and pressure, (c) Phenomena of heat conductivity under analogous circnmstances. TLe article then proceeds to select the relation between meHiug point and pressure, as a problem the experimental ditliculties of which are perhaps legist formidable; as a problem, moreover, which for thermo- dynamic reasons may judiciously be decided upon as a point of depart- ure. It develops certain general methods by aid of which increments of high melting point, however relatively small, are measurable even under conditions of very high pressure. It concludes by signaling the importance of special and preliminary researches on the measurement of high temperatures and of high pressures, with a view to the selection of such details of method as w^ill best subserve the purposes in question. Throughout the present researfih the points here mentioned have been carefully kept in mind. It is my judgment that few important steps in dynamical geology will be made until the methods for the accurate measurement of high temperatures and of high pressures have not only been perfected but rendered easily available. On the basis of this conviction the present memoir on high temperatures has been prepared; and though the experiments on temperatures may seem to have been pushed to some detail, I can not regard them either as pro- fuse or as superfluously ambitious. Indeed, if the investigation be of any fullness, it is altiost essential that the observer master the com- ]>onent parts of his research separately; and not until he has satis- factorily done this can he apply them conjointly. In work like the present, moreover, the value of the data can scarcely be determined except by the degree of uniformity of great numbers of results. In June, 1882, Dr. Strouhal resigned his charge to take a professor ship at the University of Prague. At my request Dr. William Uallock was appointed to fill the vacancy, and, being at the time associated with Dr. Strouhal in certain duties abroail, he was easily able to complete the work which the latter had been comi)elled to leave unfinished. Dr. Strouhal made the purchases of all the instruments we desired to buy in Germany, while Dr. Hallock, following my instructions, i)roceeded to purchase such apparatus as could best be obtained in France. About this time the rooms which had been placed at my disposal bj^ the American Museum at New York became temporarily unavailable. Moreover, as Dr. Elallock had joined me, more room than the museum affordegg. Ann., vol. 78, 1849, p. 112.) I will advert to the independent method of standardizing a non-in- glazed re-entrant porcelain air thermometer bulb, by thermal com- parison with a re-entrant glass thermometer bulb of known constants. Such comparison is to be made above 300^ to obviate all moisture and condensation errors, and either directly in the elliptic revolving muffle, or indirectly through the intervention of the same thermo-coui)le. The difficult estimation of the volume of the non-in-glazed bulb is thus superilnons. Again, to insure union, the gradual sagging of a weighted porcelain stem, the lower end of which has been heated to the viscous condition before the oxyhydrogen blow-pipe, into the heated neck of a re-entrant in-glazed bulb on the revolving table, has suggested itself. Similarly, atmospheric pressure may be brought to bear externally on viscous parts of bulb or stem. (Of., p. 175.) Regarding literature, I may briefly refer to a recent critical work by C. n. Bolz (Die Pyrometer, etc., 70 pp., Berlin, J. Springer, 1888), and M. II. Le Ghatelier has recently extended his valuable pyrometrie re- searches in various (lirections. 0. B. BosioHj t^cpt 1, 1889. Note. — Tlii>. t1u>rmo-f1ynan)i(' leaHonn referred to on pa^i^e 18 are briefly these: In the notation of ClaiiHiuH (Wjiriut^theoiie, 2<1 r3. ^Browne: Pyrometers; Nature, vol. 30, 1884, p. 366. 'Lauth: Mesnres pyroiuetriques li hautes temperatures; Bull. Soc. Ch., Paris, new series, vol. 46, 1886, p. 786. •Shaw : Pyrometer; Eucycl. Brit., 9th ed., vol. 20, 1886, p. 129. (677) 23 24 MEASUREMENT OF HIGH TEMPERATURES. temperatare measurement so readily suggest themselves to the student of modern physics that special attention to them is superfluous, whereas criticism of more searching value calls for special experiments. Such experiments, except in a few cases, I have not had occasion to repeat. Character of tlie measurements It is impossible to read the earlier memoirs on high temi)erature research without a feeling of uneasiness and disappointment. There is no lack of ingenious contrivances or of well-devised methods, but the results obtained are usually sadly at fault. In many cases no data for the absolute identification of the measurements made are discernible. In other cases not only do ob- servers, using different methods, fail to reach accordant results, but it is not unusual to find even skilled observers using the same method with errors in results as high as 10 per cent, for the same fixed high tem- perature datum, the l>oiling point of zinc. To secure certain facilities of manipulation Deville and Troost, at the outset of their researches, used iodine vapor as a gas for thermal measurement. This step must be regarded as a misfortune to science, and one which retarded the progress of high-temperature research many years. After the tendency of the iodine molecule to dissociate had been suspected, and the relative imperviousness of porcelain as compared with platinum air-thermometer bulbs had been clearly pointed out, the values of the boiling point of zinc begin to increase from the exceptionally low values of Becquerel (884°), and to decrease from the exceptionally high values of Deville and Troost (l,040o C.) over a total range of temperature of about 150o, until the final results of these observers (932o ami 9420, respectively) agree to about 1(P. Curiously enough, however, Weinhold, an observer of great assiduity and some experience, having made himself master of high-temperature measurement by the air thermometer methods, en- deavors to redetermine the value of the boiling point of zinc, and finds a value (1,035^) as high as the highest datum of Deville and Troost. Fortunately the subject has been rescued from this condition of vague- ness by the recent vigorous work of Violle, the results of which agree well with the mean data of Becquerel and of Deville and Troost. My chief object in giving this outline is to place before the reader the nature of the difliculties with which the problem of high temperature measurement is surrounded, and to indicate the diversity of the results reached even by the best of trained observers. Methods which in the hands of different investigators lejid to data so widely different as the values just cited are not ai)t to inspire confidence. It is perhaps more for this reason than because of real difliculties of manipulation that the gas thermometer has been so little used as a standard of reference in high-temperature measurement. For the experimental operations are not necessarily more complex than those called for in some of the empiric methods of standardization — methods which have further burdened the unfortunate subject of high -temperature research with their own allotment of vagueness of principle and inaccuracy. (078) BABUB.] METHODS OF PYROMETRY. 25 CUMsification of pyrometers, — Thermometers which depend essentially on the properties of the substance used for thermal measurement are called by Thomson ^ intrinsic thermoscopes. They may be either con- tinuous or not. it is with such intrinsic thermoscopes that practical py rometry must be conducted, although the data of the gas thermometer, as appears from the recent pyro chemical researches of Langer and Meyer,^ may safely be regarded as non-intrinsic and absolute, particu- larly in the region of high temperatures. Almost every thermal phe- nomenon has been utilized for temperature measurement, and the de- vices employed may be conveniently classified by aid of these phe- nomena as follows : I. Dilatation of soHcIr. 1. A single solid. 2. Two solids acting differen- tially. II. Dilatation of liquids. III. Dilatation of gases. 1. Expansion measured in vol- nme, manometrically. 2. Expansion measured in press- ures, mauometrically. 3. Expansion measured in vol- umo, by displacement. rV. Vapor tension. V. Dissociation. VI. Fusion. VII. Ebullition. VIII. Specific heat. IX. Hc;at conduction. X. Heat radiation. XI. Viscosity. 1. Of solids. 2. Of liquids. 3. Of gases. XII. Spectrophotometry and color. Ro- tary polarization. XIII. Acoustics (wave length). XIV. Thermo-elec tries. XV. Electrical resistance. XVI. Magnetic moment. XVII. Miscellaneous. Dilatatian of solids. — Curiously enough the dilatation thermometers were not the first to suggest themselves. Newton, in his scala graduum caloris, proposes a method of temperature measurement based on his law of cooling, almost as early as 1700. However Musschenbroek (1731), Ellicot (1736), Bouger (1745), and others availed themselves of single- bar expansion devices, and Mortimer made a thermometer on this prin- ciple in 1746. The most celebrated apparatus of this kind (1782) is Wedgwood's' pyrometer, in which the attempt is made to express temperature in a scale based on the shrinkage exi>erieuced by a little compressed cylinder of clay after exposure to the said temperature. This apparatus came into much more general use than its inventor intended. Its indications were vigorously discussed by the physicists of the time, especially by GuytonMorveau,* who in attempting to convert Wedgwood's arbitrary thermal scale into degrees centigrade showed the apparatus to be un- » Encyclopedia Brit., 9th ed., vol. 11, IBHO, p. ^0. ^Langer and Meyer, Pyrochemische Untersuchangen, Braanschweig, Vieweg n. Sohn, 1885; Berl. Ber., vol. 18, 1885, p. 1501. » Wedgwood: Phil. Trans., Roy. Soc, vol. 72, 1784, p. 305; vol. 74, 1782, p. 358; Dingler's Jour., vol. 15, 1824, p. 230. * Gnyton-Morveaa : Annalos dc chimie, Paris, Ist series, vol. 46, 1803, p. 276; ibid., vol. 73, 1810, p. 254 ; ibid., vol. 74, 1810, pp. 18, 129 ; ibid., vol. 90, 1814, pp. 113, 225. (679) \ 26 MEASUREMENT OF HIGH TEMPERATURES. reliable because of the tendency of clay to shrink irregularly and to warp, and because of its dependence on the kind of clay used and on the time of exposure. After this the use of single-solid pyrometers seems to have been abandoned until quite recently, when Mr. Nichols,* in comparing the resistance- temperature formulae of B^noit, Siemens, and Matthiessen with his own, found the linear dilatation of platinum very serviceable for the co-ordination of his data. lie gives i)reference to the expansion thermometer over the resistance thermometer whenever the special constants of both instruments are unknown. The absence of further devices for single-solid pyrometry is not re- markable when the vast numbers of pyrometers in which solids are com- bined diilerentially are taken into view. Some of the earliest attempts of this kind are due to Borda,^ although Guy ton-Morveau (loc. cit.) was probably the first observer who had pyrometric ends in view, the solids adopted being platinum and porcelain. This physicist was at some pains in systematizing the dilatation of solids. More elaborate attempts .to utilize the occurrence of diflfereut expansibility in solids for pyro- metric purposes are due to Daniell.^ Daniell's substances are platinum and black lead, with a suit^ible interposition of clay, and his work on the dilatation of solids is elaborate, but unfortunately without much permanent value. Following Dauiellcome a host of inventors whose apparatus, though often exceedingly ingenious, have only technical importance. These may therefore be passed over with a single brief mention here. Peter- sen^ has a platinum wire in an iron tube ; Gibbon^ exposes rods of iron or steel, and copper provided with a contact lever; Oechsle^ utilizes an iron-brass spiral working on the principle of Br^guet's metallic ther- mometer, while Clement^ replaces the metals of such a spiral by plati- num and silver. Prinsep,^ however, held that even this apparatus is not reliable on account of the tendency of the metals to alloy — a con- clusion which has WeinholdV assent. Gauntlet,'® Desbordes,^^ Oechsle," * E. L. Nichols: Am. Jour. Sci., 3d series, vol. 22, 1881, p. 363. 'Borda: Bolt Traite, I, 1816, p. 159. The use of iron and brass seems first to have been made by Felter in Braunschweig. ^Daniell : Experiments with a new register pyrometer for measuring the expansion of solids; Jour. Royal Soc, London, vol. 11, p. 309; Philos. Mug., London, 2d series, vol. 10, 1831, pp. 191, 268, 297, 350; ibid., 3d series, vol. 1, 1832, pp. 197,261; Din- glor's Jour., vol. 19, p. 416; vol.43, p. 189; vol. 46, pp. 174,241. ^Petersen: Gebler. Phys. Worterb., 2d aeries, vol. 7, p. 994. ^Gibbon: Dingler^s Jour., vol. 68, 18:}h, p. 4:J6. <^^Oechsle: Ibid., vol. 60, 1836. p. 191. "Clement: Ibid., vol. 80, 1843, p. 241. *" Prinsep: Ibid., vol. 28, 1828, p. 421. « Weinhold: Dingler^s Jour., vol. 208, 1873, p. 125. »o Gauntlet: Ibid., vol.157, 1860, p. 279. »» Desbordes: Ibid., vol. 157, 1860, p. 279. »aOech8le: Ibid., vol. 160, 1861, p. 112; ibid., vol. 196, 1870, p. 218. (080) «»^RU»1 METHODS OP PYROMETRY. 27 Bock,^ Lion ami GuicliarcP use iron and copper or iron and brass, either in the form of paiallel rods or tubes bundled together or of a rod within a tube; in each case provided with a suitable index and dial arrange- ment. A like apparatus of metal and fire-clay (chamotte) is due to Bussius.^ Finally, the use of graphite for pyrometry, an idea which long ago occurred to Daniell, was resuscitated by v. Steinle and Har- tiug.* In their apparatus an iron tube surrounds a rod of graphite, and an ingenious mechanism permits only those parts which are actually exposed to the high temperature to act diflferentially on the dial. Ad- justment is made by means of mercury. Winkler, who first tested tbese apparatus, declared them serviceable, but his testimony is not corrobo- rated by Beckert. He finds that the indications of graphite pyrometers are neither strictly comparable nor very decisive, and that they are quite unreliable above 6OO0. Tbis criticism api)lies to the pyrometers of the present class generally. Dilatation of liquids. — Pyrometers based on liquid expansion are few in number and quite unavailable. An old apparatus is described anony mously in Dingler's Journal* in which the expansion of a fused alloy in a porcelain bulb is registered by aid of a platinum rod moving alqng a scale. The division is in Wed *j: wood degrees. A similar apparatus was proposed by Achard.^ Here the expansion of the alloy is to be read off directly in the translucent stem of the porcelain bulb. The construction, therefore, is that of the ordinary mercury thermometer. I doubt whether either of these instruments has ever been used. Person^ applied a new principle. He found that mercury under 4 atmospheres pressure boils above 450^, under 30 atmospheres pressure above 500^ ; that the dilatation in these cases is quite notable. Here I may refer to experiments of Bystrom,^ to whom a hydro- pyrometer is due, and to Waterston,^ by whom the expansion of water at high temperatures (300°) under pressure has been specially investigated. Waterston formulates his data and is led to the striking result that water at 300^ expands at a greater rate than permanent gases. Water at high temperatures and pressures attacks glass, rendering it opaque and thus putting an end to the experiment. Dilatation of gmes (manometric methods). — According to Shaw^® a rudimentary air thermometer was built by Amonton in Paris about as •Bock: Ibid, vol. 195, 1870, p. 312. 2 Lion et Guichard : Ibid., vol. 220, 1876, p. 37. 3 B.U88iu8 : Ibid., vol. 164, 1862, p. 107. Berg- und Hilttenm. Zeitiing, No. 10, 1862. * V. Steinle and Harting : Clemeus Winkler's report in Zeitschr. fUr Analyt. Chem., vol. 19, 1880, p. 63; Beckert'e report in ibid., vol. 21, 1882, p. 248. * Dingler's Jour., vol. 32, 1829, p. 355. «See Becqnerel: Ann. ch., 3d series, vol.78, 1863, p. 52. ' Person : Comptes Rendus, vol. 19, 1844, p. 757. » Bystrom : Berl. Ber., 1862, p. 344. "^ Waterston : Philos. Mag., Lond., 4th series, vol. 26, 1863, p. 116. io£nc. Brit., voL 20, 1886, p. 129. (681) • 28 MEASUREMENT OF HIGH TEMPERATURES. early as 1700. Gujtoii-Morveau,^ in whose thermal researches the dila- tation of solids and the specific heat of idatiniim were discussed with reference to their availability in thermal measurements, also proposed jfases for tliat purpose. Prinsep,* however, appears to have been the first to construct an air thermometer and to Apply it as an instrument of research. Prinsep's bulb was of gold. This was in pneumatic con- nection with a reservoir of olive oil provided with a sensitive manome- ter. As the air in the bulb expanded it displaced the oil which exuded through a cock at the bottom of the reservoir. Pressure being main- tained constant the amount of olive-oil discharged is equal in bulk to the amount of air which enters the receiver at the given temperature. Hence by weighing the oil the temperature of the bulb may be calcu- lated. Prins^p's apparatus is unique, and his absolute thermal data are very much nearer the truth than those of his predecessors. Indeed they compare well with the known data of the present day. Priusep's chief data refer to the melting points of alloys of gold, silver, and pla- tinum which bear his name. To these 1 shall recur. Leaving Davy,^ who constructed an air thermometer in which the air expansion was weighed in mercury, and Mill* and Petersen,^ to whom also* forms of air thermometers are due, the next observer seems to be Pouillet.^ Pouillet's researches are of prime importance. Having con- structed a bulb of platinum, which enabled him to reach the highest tem- peratures, he then took the first definite steps in radiation-pyrometry by investigating the temperature at which solids glow, in calorimetric pyrometry by determining the specific heat of platinum between oo and 1,200°, aiid in .thermo-electric pyrometry by carefully calibrat- ing a thermo-couple of iron and platinum. As these apparatus will be referred to again, I need only remark here that to Pouillet the form of constant pressure manometer is due very nearly as it is to be used in pyrometric work to-day. This apparatus was perfected by Regnault,"^ anerature8, availed themselves of bulbs of copper and of i)latinnm for their thermal measurcineuts. These were used much after the inanuer of vapor-density bulbs. The long capillary necks could be closed at the desired temperature by a faucet, and the temperature was then calculated from the amount of water which en- tered the cold bulb. These experiments form a natural transition to the earlier researches of Deville and Troost,^ in which a splendid improvement in thermal measurements was uiade possible by the in- troduction of porcelain bulbs to replace those of metal and of glass. Deville and Troost here use Dumas's well-known method to evaluate both temperature and vapor density. In their search for a heavier thermal gas than air they select iodine vai>or preferably to mercury, . inasmuch as the metal is apt to condense on the colder parts of the bulb and in falling down upon the hot parts to cause fracture. Using this iodine thermometer, they find that cadmium and zinc boil at 86O0 and 1,0400, respectively. They also measure the coefficient of expan- sion of i)orcelain by noting the length of the necks of their bulbs at different (high) temperatures (Oo, 86O0, l.OOOO). Having found these data they proceed to the measurement of vapor densities, with results which are not of interest here. The high values for the boiling point of zinc thus obtained conflicted very seriously with certain measurements subsequently made by Bec- querel.* This observer used a ]>latinum-])alladium thermo-couple, the indications of which had to be carefully referred to Ppuillet's plati- num air thermometer. In this way Becquerel found the boiling point of zinc at 932o, more than 100° below that of Deville and Troost, as well as reaching a similarly low boiling point for cadminni, 746o. In the same paper thfi method of determining a series of melting points of metals is described and the data are fully given, and several final sec- tions are devoted to radiation pyrometry. As reganls accuracy of measurement and varied character of results, this paper is one of the most important in the history of pyrometry. It is to be noticed that Becquerel was aware of the i)robable permeability of platinum to gases at high temperatures. Further mention will be made of this later. These discordant results necessarily i)rovoked considerable discussion between BecquereP and Deville and Troost,^ which temporarily resulted in favor of the former. Deville and Troost naturally reject Becquerel's low values, and be- * Dev'iUji et Troost : i>ur la densit^S do vaiMMir d'un certain norubre de niaticro.s luin- erales; C. R., vol. 45. 1857, p. H21 (C. F. Berl. Ber., 1857. p. 73) ; C. R., vol. 49, 1859, p. 239; Ann. ch. et phys., 3d series, vol. 58, 1800, p. 257. 2 Becquerel: Recherches siir la determination des hautes temperatures. Ann. ch. et phys., 3d series, vol. 58, 18(/3, j). 49. 'Becquerel: C. R., vol. 57, 1863, p. 855; Inst., IBCkJ, p. 369; C. R., vol. 57, pp. 902, 925; Inst., 1863, p 385. ♦Deville et Troost: C. R., vol. 56, p. 977; Inst., 1863, p. 161; C. R., vol. 57, 1863, pp. 894, 935; Inst., 1863, p. 377; ibid., p. 897. (683) 30 MEASUREMENT OF HIGH TEMPERATURES. lieve them to be erroneous because of the permeability of platinum at high temperiitures. In doing this they refer to researches of their own* on the porosity of metals. Becquerel's reply is of an experimental character. He continues his work on air-thermometer i>yrometry, re- placing the platinum bulb with bulbs of porcelain, and availing himself both of constant pressure and of constant volume methods of measure- ment. Curiously enough the results of these new determinations are even below the former values, the boiling points of zinc and of cadmium being at 891^ and 720^, respectively, while for the former as low a value as 884° was found. Becquerel dwells upon the excellence of the Pou- illet method for high temperatures. Deville and Troost nevertheless refuse to regard these new results of BecquerePs as conclusive. They insist upon the impossibility of deriving accurate data with a porous reservoir. They point out that the large difference between BecquerePs pn^sent and former results is in itself to be looked ui)on with suspicion. They finally assert, inasmuch as BecquerePs i)yrometers were not in immediate contact with zinc vapor, but were exjiosed in a closed lateral tube which issued from the zinc retort, that the datum measured is not the boiling point of zinc but a temperature below it. They finally re- peat their own experiments with the same values as before. Becquerel again endeavors to show that the permeability of platinum did not se- riously influence his results. He shows that his own researches are made in a way calling for much less skilled manipulation than those of Deville and Troost; and he finally adds that Deville and Troost have made but a single measurement with air, and that the use of iodine vapor as a gas for thermal measurement is not immediat«.*ly warranted. Becquerel states the reasons for considering his boiling-point apparatus sufficient, but agrees that a possible error may be tlie impurity of his zinc. With these remarks discussion ended, being left without a final issue; but it is well to state, in passing, that the results of subsequent observers, including Deville and Troost themselves, have proved be- yond a doubt that the later inferences of BecquerePs were very nearly correct. Victor Meyer,* I believe, was the first to suggest the possible dissocintion of the iodine molecule at high temperatures, a behavior which he had established for chlorine. Meyer's views were corrobo- nited and variously interpreted by Crafts and Meier,^ by V. Meyer him- self,* Crafts,^ Troost,® Berthelot," and others.^ * DeviUe and Troost: Porosit<5 . -v. and C. Meyer: Berl. Bcr., v«)l. l*i, 1879, p. U)H\. ^Crafts and Meier: C. R., vol. 90, 1^80, p. GOO; Berl. Ber., vol. l;J, 18;:j0, p. 851. n^ Meyer: Berl. Ber., vol. 13, 18^<0, p. 391; ibid., 18hU, p. 1010. » Crafts: Ibid., 1880, p. 1310. "Troost: C. R., vol. 91, 1880, p. ri4. 'Bertbelot: ibid., p. 77. "Cf. Deering: Cbeni. News, London, vol. 40, 1879, p. 87. (684) BABUB.J METHODS OF PYROMETRY. 31 In 1863 Deville and Troost ^ began the publication of another series of investigations on high temperatures and boiling points. They describe their new porcelain air thermometer bulb, which is a hollow sphere of porcelain, glazed both within and without, with a short neck, to which a capillary fissureless porcelain stem is soldered with feldspar, and the oxy hydrogen blowpipe. They proi>ose to discard iodine and to use air' in its place, giving their apparatus a form nearly identical with Regnault's* normal air thermometer. They insist on the importance of spherical bulbs, and the air contained is dried at red heat by aid of a vacuum pump. All the zinc is carefull3' purified, and used in large quantities (charges of 17 kg.). It is but just to add here, to the great credit of Deville and Ti'oost, that the actual construction of the porce- lain air thermometer occupied them for nearly seven years, working in concert with M. Gosse, in charge of the porcelain works at Bayeux. They were the first to use metallic vapor baths for constanVhigh tem- peratures, a method which has been adopted by Becquerel and by physicists generally since that time. In 1864 Deville and Troost^ i)ro- ceeded toward. the accurate measurement of the heat expansion of the Bayeux porcelain. Using a jmrcehun bulb simultaneously and of the same material as the porcelain of the dilatation apparatus, they have the data sufficient to eliminate the error due to heat expansion Irom the thermal measurements made. Their method is necessarily one in which the linear expansion of a porcelain rod exposed in a zone of known constant temperature is measured by the cathetometer. Two platinum buttons, inserted in the entls of the stem, subserve tbe purpose of fiducial marks, and they are viewed through long lateral porcelain sight-tubes in the constant temperature ai)paratus. In this way they show that in some 200 measurements the cubical expansion of i>()rcelain, between Oo and l,600o, is 0.000016 to 0.000017. Above l,o00o it be- comes rapidly larger. In addition to this normal heat expansion, porcelain experiences permanent dilatation, as is proved both by measuring the linear dimensions and by density tests ai)plied to the porcelain after heating. Curiously enough, this density diminishes with frequent heating. The permanent expansion, which is a very serious error in the first heating (the volume of a bulb increasing fron) 281.3*^® to 285.6^*' in six heatings, for instance), fortunately, soon be comes negligible. Deville and Troost, at the end of their work, justly congratulate themselves on these results: " Nous conclurons que la por- celaine de Bayeux, matiere absolumeut imperm<3able et encore rigide aux 1,5000 ♦ ♦ » capable de se dilater jusque h\ d'niie manit^ro uni- forme, sans qu'on ait j\ tenir compte de sa dilatation i)ermanente si ce n'est au butdes experiences." They again emphasize the excellence of soldering together, with feldspar in the oxyhydrogen flame, the accu- rately calibrated bulb and stem. ' Deville and Troost, vol. 57, 18(>:{, p. 897. - Regnault: loc. cit., PL I, Figs. 7, et seq. » Deville find TrooHt: V. R., vol. r>9, 1864, p. 162. (685) 32 MEASUREMENT OF HIGH TEMPERATURES. r Aller these publications Deville and Troost made no further impor- tant contributions to high temperature thermometry for five years. The subject occupied Regnault,* who proposed two methods. Th© first of these small flasks of iron or porcelain are partially charged with mercury, and closed above with a loosely-fitting valve or stopper. These are exposed at the temperature to be measured, and this is calculated from the weight of mercury left after cooling. The other method, being a displacement method, will be described below. Shortly after this a series of very painstaking attempts in the measure- ments of high temperatures were made by Schiuz.^ Curiously enough, these papers, which contain a series of experiments admirably correct in principle, are but little known. Schinz, after endeavoring in vain to utilize the principles of heat conduction in practical pyrometry, and after testing Reguault's displacement method with unfavorable results, applies the thermo-electric methods of Pouillet and of Becquerel. Schinz's air-thermometer bulb is a huge iron cylinder, from the center of one end of which an iron capillary tube passes to the manometric ap- paratus, while an iron tube for the insertion of the junction of the thermo-couple projects inward to the center of the figure through the other end of the cylinder bulb. In this respect Schinz's thermometer is unique, being the only form of re-entrant bulb hitherto devised. The great advantage of this form of bulb, which, quite independently of Schinz, has been perfected in my experiments, will be emphasized below (Chap. IV). Nitrogen is the thermal gas in Schinz's work, and the cali- brations are carried svs far as l,000o. Giving him full credit for correct- ness of method and for the assiduity with which he endeavored to carry it out, Schinz's aijparatus was doomed to fail because of its impractical clumsiness of construction, to say nothing of the permeability of iron at high temperatures. It is not possible to make much definite progress in the measurement of high temperatures with an apparatus which falls shortof the conditions of facility and certainty of manipulation. I shall revert to these measurements. For the special conveniences of the in- vestigating chemist, Berthelot^ devised an apparatus intended to be compact and very sensitive, and provided with an easily adjustable em- piric scale. His instrument is based on the expansion of air and grad- uated by boiling points. Another instrument by Zabel* is so adjusted as to ring an electric bell at any given temperature. It is perhaps ex- pedient to advert in this connection to the thermometers of Weinhold* and of Crafts,^ both of which are constructed on Jolly's' i)lan, but so ad- justed that the conditions of constant volume are secured by the aid of ^ Regnault: Ann. ch. ot phys., 3d series, vol. 63, ItiHl, p. 39. » 2 Schinz: Dingler's Jour., vol. 177, 18G5, p. 85; ibid., vol. 179, 1866, p. 436. 'Bertliolot: Ann. ch. ct phys., 4th siiries, vol. 13, 1868, p. 114. *Zabel: Dingler's Jour., vol. 195, 1870, p. 236. '^Weinhold: Pogg. Ann., vol. 149, 1873, p. 1^H). * Crafts: Ann. do Chim. et do Phys., 5th series, vol. 14, 1878, p. 409, •Jolly: Pogg. Ana., Jubelbaud, 1874, p. 82. (680) BiLBua] METHODS OF PYROMETBY. 33 an electro-magnetic engine. The mechanism of Grafts' new thermome- ters appears to be particnlarly perfect in this respect. An air ther- mometer in which the pre8sure is directly measured manometrically ts described by Codazza.^ A rigorous investigation of the formula of the air thermometer, with a view toward the construction of an apparatus of exceptional delicacy, has lately been made by Grassi.^ Finally, the possible condensation of gases on metallic air thermometers of very large internal surface has been incidentally discussed by Fuess.^ Op- erating with bulb in form of a cylindrical ring, Fuess found that for a correct ice point the boiling point of water showed a value enormously high, which gradually decreased without reaching a normal value. His research is unfinished, however, and thus the full interpretation of these anomalous results is yet to be given. After the earlier work of Deville and Troost and the papers of Schiuz, the most important memoir on high temperature measurement was published by Weinhold.^ Having discussed the important methods of empirical pyrometiy, with reference to their availability for practical work or for research, Weiuhold uses his air-thermometer for a rede- termination of the boiling point of zinc. Unfortunately his high value, 1,0360 at 71.80^", which is only a little below the erroneously large values of Deville and Troost, casts a slur over much of Weinhold's elaborate experimentation, and his criticism on the merits of Siemens' pyrometer, of calorimetric pyrometers, and of the dissociation pyrome ters fail to obtain the consideration which they probably deserve. Weinhold's bulb is of Meissen porcelain and his instrument of measure- ment is a modified Jolly thermometer. In this place it is well to call attention to certain experiments com- menced at about this time by Amagat and others to test the correctness of Boyle's law at different temperatures and high pressures. The con- stants hitherto adopted in high temperature air thermometry for all temperatures and pressures indiscriminately were those investigated by Kegnault' and by Magnus.® By Amagat,^ Cailletet," and others these researches were pushed to great nicety for pressures as high as ^Codazza: Dingler's Jour., vol. 210, 1873, p. 255. * Qrassi : Rend. delP Academia delli Scionze fisiche e math., vol. 24, pp. IG, 131, 1885. BeiblStter, vol. 10, 1886, p. 387. *Fae88: Zeitscbr. fUr InstrumeDtenk., vol. 5, 1885, p. 274. ^ Weinhold: Osterprogramm der boh. Geworbcscb. zu Cbemnitz, 1873; Pogg. Ann., vol. 149, 1873, p. 186. * Regnault : Relation des experiences, Paris, 1847, pp. 15, 168. ^Magnns: Pogg. Ann., vol. 55, 1842, p. 1. » Amagat: Fortscbr. d. Pbys., 1869, p. 155 ; C. R., vol. 71, 1870, p. 67 ; C. R., vol. 73, 1871, p. 183; Archives bcL, pbys. et nat. Geneve, 2d series, vol.40, 1871, p. 320; Ann. cb. et Pbys., 4tb series, vol. 29, 1873, p. 246; ibid., 5tb series, vol. 22, 1881, p. 353, etc.; C. R., vol, 94, 1882, p. 847 ; C. R., vol. 95, 1882, p. 638 ; C. R., vol. 99, 1884, pp. 1017, 1153; C.R., vol. 103, 1886, p. 429. •Cailletet: C. R., vol. 70, 1870. p. 1131. Bull 54 3 (687) 34 MEASUREMENT OF HIGH TEMPERATURES. 500 atmospheres and for temperatures below 300<^, and in the hands of Amagat they led to the discovery of minima of " pv." These researches^ which mast be passed over briefly here, are not as yet in a state of prog- ress to enable the results to be at once applied. It is therefore reassur- ing to find in the labors of Langer and Meyer^ a number of data tending to show that at high temperatures and for moderate pressures the con- stancy of the co-efficient of expansion of gases may be warrantably assumed. To return fh)m this digression to the subject in hand I find an im- portant research by Erhard and ScherteP in which the melting points of Prinsep's alloys are again carefully determined by the porcelain air thermometer. The bulbs are of Meissen porcelain, and the method of measurement is essentially that of Weinhold. Finally, in 1880, De- ville and Troost ^ publish a succinct account of their results in high temperature measurement, and thus conclude the interval of compara- tive silence.^ They describe a new form of air thermometer, apparently superior to the Eegnault normal form. In this instrument the air of the bulb is transferred into the measuring apparatus by a Sprengel's pump. The bulb itself, being placed in a furnace fed by heavy x>etroleum oil, can be heated to any desired temperature by supplying a greater or smaller amount'of fuel, through a graduated stop-cock. To eliminate the stem error they again use the <' compensator," which is a closed porcelain capillary tube identical with the stem of the air thermometer and exposed side by side with it. This compensator is provided witli its own manometrio attachment. Nitrogen is used preferably to air. The last memoir contains a full digest of their results on the boiling point of zinc. The methods of experiment and of measurement are also tersely given in chronological sequence. The authors put great stress on the purity of their zinc, on the fact that no iron was used in the re- torts, on the great mass of zinc distilled (17 kg. to 20 kg.), on their methods of protecting their bulb from direct radiation by multiple screens, and on the great heat of the circumambient flame. The porce- lain bulb, its peculiarities, and its construction are described with some detail. Their mean value for the boiling point of zinc, as Troost' sub- sequently remarks, is 942^, and the number of measurements made, 27. In some experiments made at a later date by Troost^ the boiling point of selenium was found between 664^ and 683^, the determination being feasible in a vessel of enameled irbn. Troost ^ therefore concludes that > LaDger n. Meyer : Pyrochemische Untersnohnngeii) 1885. 'Erhard and Schertel: Jahrbach filr das Berg-and-HUtteu wesen, im K5nigr. Saoh- een, 1879, p. 154. 'Deville et Troost: C. R., vol. 90, 1880, pp. 727,773. ^Deville: C. R., vol. 74, 1872, p. 145; is speculative, and refers to excessively high and to solar temperatures. ^Troost: C. R., vol. 94,1882, p. 788. « Troost: Ibid., p. 1508. ▼Tioost: Ibid., vol. 95, 1882, p. 30. (688) BABU8.) MBTUODS OP PYBOMETRY. 35 vaiK)r densities iu selenium vapor may safely be made in vessels of re- fractory gl£^s, and reconimends for that purpose the glass of Appert fr^res h Olichy, which is nearly rigid at this temperature. Other rele- vant results of Troost* on the permeability of platinum to hydrogen aud of silver to oxygen at high tem|)erature have been adverted to. Beithelot^ points out the occurrence of unstable platinum hydrides. The value of the boiling point of zinc, to which the later researches of Deville and Troost had given a value compatible with that of Becque- rel, was soon to be further fixed in position by the research of Violle.^ Using a triple jacketed boiling point apparatus of enameled iron, he found by Deville and Troost's methods that zinc boils at 930^, thus giving further warrant to the data of Becquerel and Deville and Troost. In view of the accordance of these data, the problem of high temperature measurement may be regarded as solved with some accu- racy as £eu* as 1,50(P. The greater share of the credit for this result is undoubtedly due to Deville and Troost, notwithstanding their unfortu- nate beginning and the fact that they allowed the subject to slumber in their hands for so many years. Yiolle refers to the problem of mere high temperature measurement as being one of great simplicity, and finds his main difficulty in the construction of constant temperature apparatus. My experience is the reverse of this. It is not very difficult to get the zinc point; but it is difficult to obtain thoroughly accordant values for it when different bulbs are used. Yiolle, who used but a single bulb (so far as I have been able to make out), obtains val- ues which are almost identical, but which really apply only to the par- ticular bulb in hand. The error possible in measuring the constants of the bulb is one of a very serious kind, and in case of a single bulb it remains arbitrarily fixed. The data of Deville and Troost, which were obtained by using a large assortment of bulbs, bear evidence to this. The differences between their later results are by no means insignifi- cant, and these observers were most scrupulous in perfecting their methods, even to the fine points of experimental detail. Becquerel, in using divers thermometer bulbs, encountered the same wide limits of error. Regarding Becquerel's later and very low values, moreover, it is probable that the criticism of Deville and Troost applies. Becque- rel's boiling-points apparatus was imperfect. In the case of so large an object as the air-thermometer bulb, at so high a temperature as the boiling point of zinc, ite data can nof be regarded as identical with the temperature of the vapor unless it be in actual contact with it. Evi- dence bearing on all these points will be repeated in Chapter lY. Eegarding Deville and Troost's experiments on the coefficient of ex- pansion of porcelain,- a short critical remark relative to the occurrence of permanent dilatation is in place here. When a porcelain rod is sus- > Troost: Ibid., vol. 98, 1884, p. 1427. ^Bertbelot: Ann. ch. ot phys., .5th series, vol. 30, 1883, p. 530. 3Violle: C. E., vol. 94, 1882, p. 720. (689) 36 MEASUREMENT OF HIGH TEMPERATURES. peiided at one end and heated to extreme whiteness, it is probable that some permanent elongation will occur by virtue of the viscosity of the hot roil. The question therefore occurs whether this permanent expan- sion may not to some extent have produced the dilatation due to vitri- fication which they observed, or have been partially confounded with it. Messrs. Deville and Troost were careful to test the specific gravity of their heated porcelain, and they found a dimunition of density, a re- sult in harmony with the dilatation observed. Again, the fact that per- manent expansion vanished after successive heating in their ezperi- mentB is evidence in their favor. And yet I regard this remark not superfluous, because, in my own experiments, in which careful volumenometric tests of the volume of the bulb after successive heatings to l,000o or l,200o were made, I ob- served no permanent dilaterature measurement. Optic, calori- metric, and electrical methoils of temperature measurement, they con- tend, are all dependent on the air thermometer, the results of which are reliable only in the case of very perfect mechanism, and are not available above the temperature at which porcelain is rigid. By inserting a capillary platinum tube into the neck of Meyer's apparatus the air can be lifted out by a current of carbonic acid gas or of hydrochloric acid gas, both of which are easily absorbed. It is possible to make va])or density measurement to alternate with thermal measurements; and since the operation may be completed in two minutes, absolute rigidity of the porcelain vessel is not rigorously essential. Entering into the spirit of this suggestion, Meyer^ and his pupils opened a new field of pyrochemical research, in which, after establishing the constancy of the coeflBcient of expansion of permanent gases at high temperatures, they extend their inquiries further to vapors. Meyer's apparatus hero is a hollow sphere of porcelain provided with axial capillary tubes for inilux and efflux of gas. Following Meyer's summary, the linear character of the heat expan- sion of gases at high temperatures (barring dissociation) is to bo regarded as established for selenium and tellurium (Deville and Troost), for nitrogen, oxygen, mercury vapor, and Asg O3 vapor (V. and C. Meyer), for hydrochloric acid, and carbonic acid gas (Crafts), and for hydrogen (Meyer and Zttblin). These inferences antagonize the pub- lished opinion of Troost,* who, with Berthelot's acquiescence, prefers to regard the expansion of gases at high temperature (iodine for instance) as a physical function of temperature rather than to accept the occur- rence of dissociation. Meyer* and his pupils, however, push their investigations into much greater detail, adding to the number of gases of constant thermal c >- efficient and interpreting the variable behavior of others. Their new researches are carried on at temperatures even as high as l,700o. Their apparatus is a long platinum tube provided with terminal capillary stems of platinum which have been ground into the somewhat narrower ends of the tube. This therm ometric tube is surrounded by ftre-chiy which in its tutu is enveloped by a second and wider platinum tulu'. »V. u. C. Meyer: Berl. Ber., vol. 12, 1879, p. 1426. "Crafts and Meier: C. R., vol. 90, 1880, p. 606. »Meyer: Berl. Ber., vol. 13, 1880. p. 2019; ibid., vol. 15, 1882, p. 1161. ^Troost: C. R., vol. 91, 1860, p. 54. ^LaDger u. Meyer: Pyrochemi.iclie Untersnchangen, Braunschweig, Vicweg u. Sohn, 1885; Berl. Ber., vol. 18, 1885, p. 1501. (691) 38 MEASUEEMENT OP fflOH TEMPERATURES. To obtain the high temperatures in qaestion retort carbon is bnmeil in an air-blast. The displacement method shows that oxygen, nitrogen, sulphurous acid, aud even carbonic dioxide are stable at l,700o. Phiti- num absorbs much oxygen and must be saturated with it before the ther- mal measurements are commenced. On the other hand, chlorine, bro- mine, iodine, carbonic oxide, steam, and even hydrochloric acid are more or less dissociated. Following these researches into further conse- quences, Meyer and his pupils^ determine the vapor density of zinc, prov- ing that all known metallic vapors are monatomic, and they even meas- ure' tbe vapor densities of antimony, phosphorus^, and arsenic, at l,437o. These brilliant researches contain the most advanced work thus far ' done on the subject of high temperatures, and it is upon the validity of some of their results, the non-dissociative character of the expansion of the permanent gases at high temperatures, that all hi^h temperature thermal measurement depends. Vapor tension, — Pyrometers of this kind have received little attention. Sajotschewsky^ pointed out that the vapor tensions of different quanti- ties of liquid are identical as far as the absolute boiling point, after which the curves diverge. He further studied the temperature and pressure relation of twelve liquids in detail, at least as far as the critical point. The importance of vapor tension thermometers was signalized by Sir William Thomson,* but the remarks refer principally to low temperatures. Shaw* has recently inquired somewhat rigorously into such pressure-temperature relations. For moderately high temperatures CraftsV paper seems to be the only companion research to Sajots- chewsky's. Crafts studied the boiling point and vapor tensions of mercur^^ and sulphur vapors, as well as of some carbon compounds with his hydrogen gas thermometer. DisHociation, — The difficulty in the. way of a successful application of vapor tension thermometers, Lamy believed to have been overcome in his dissociation thermometer. In the suppositive case of marble, for instance, originally placed in a vacuum, the pressure due to the evo- lution of carbonic dioxide will increase with temperature, and would finally revert to the pressure zero when the original temperature is again reached. Debray V data for the dissociation of calcic carbonate and Isambert's^ further researches on the gaseous dissociation of solids, suggest a number of materials. Lamy^ incloses these in an exhausted »Men8ching u. Meyer: Berl. Ber., vol. 19, 1886. p. 3295. ^Mcusching u. Meyer: Giitt. Nachr., 1887, p. 258. ' Sajotschoweky : Beibluttcr, vol. 3, 1879, p. 741. < Thomson: Proc. Royal Soc, Ediuburgh, vol. 10, 1880, p. 532. '^Shaw: Trans. Cambridge Phil. Soc, Eng., vol. 14, 1885, p. 30. eCrafts: Nature, vol. 2G, 1882, p. 4(H5. '^Debray: C.R.,vol. 64, 1867, p. 603. ^Isambort: These pr<$sento ;\ la Faculty des sciences de Paris, 1868. oLamy : C. R., vol. 69, \m% p. 347 ; vol. 70, 1870, p. 393. Diiigler's Jour., vol. 194, 1869, p. 209 ; vol. 195, 1870, p. 525. BABUB.) METHODS OF PYROMETBT. 89 porcelain bnlb. Weinhold (loc. cit) who examined this apparatns con- demns it, at least so far as the ^^ pyroni^tre ii niarbre^ is coucerned. It appears that the carbon dio^de emitted is not again absorbed with saflBlcient regularity to subserve the purpose of thermal measurement. Perhaps Troost's^ diffusion method for studying high temperature dis- sociation is to be added to this paragraph. lf\man. — These pyrometers are discontinuous as well as intrinsic. Nevertheless, in virtue of their simplicity they are among the most serv- iceable of all the forms of pyrometers devised. As long ago as 1828, Prin- sep,' using an air-thermometor bulb of gold, endeavored to measure the melting points of silver-gold, silver-platinum, and gold-platinum alloys. The brothers Appolt^ investigated similar data for copper-tin alloys, using a calorimetric thermometer for high temperature measurement. A special double crucible for fusion of silver-platinum alloys is given by Heeren.^ Temperatures estimated by alloy fusion were largely made use of by Plattner. ^ Becquerel,^ in his extended paper on the measurement of high temperatures, gave considerable attention to melting points. He used metallic wires and measured the fusing temperature with his calibrated thermo-couple. After him, Biemsdyk^ made a series of meas- urements on metallic melting points. A very ingenious series of ring- shaped cups, placed on a common axis in a tier, was suggested by Heeren.^ These cups contain rings of alloy, the consecutively varying melting points of which are stamped on the bottom of the cups. After each observation the rings are simply turned. Carnelley^ made use of fusion pyrometers, substances of known melting points being inclosed in capillary tubes to serve for the identification of similarly exposed substances of unknown melting point. Results on the melting points of platinum alloys are due to Eoberts.^ A more elaborate series of re- searches is due to Violle,^® whose data for high melting points are pre- sumably the best in hand. Violle makes a careful study of the relation between specific heat and temperature. Assuming this relation to hold as far as the melting point in each case, he fixes this point for silver (9540), gold (1,0350), copper (l,054o), palladium (l,500o), platinum (l,775o),and iridium (1,950^), calorimatrically. For metals which melt below the platinum point, either the metal itself or platinum may be 1 Troost : C. R., vol. 89, 1879, p. 306. ^PriDsep: TraDS. Royal Soc, London, 1827; Ann. ch. ot phys., 2d series, vol. 41| 1829, p. 247; Pogg. Ann., vol. 13, 1828, p. 576; vol. 14, 1828, p. 529. ^Mitth. des Gtowerbe Vereins fur Hanover, 1855, p. 345. *Heeren: Dingler's Jour., vol. 161, 1861, p. 105. ^ Becquerel : Ann. ch. et phys., 3d. series, vol. 68, 1863, p. 49. <*Riem8dyk: Jahresber. d. Chem., 1869, p. 993; Chem. News, LondoD, vol. 20, 1869, p. 32. * Heeren : Zeitschr. des Vereins d. Ingenieare, 1876, p. 314. •Carnelley: Joar. Chem. Soc, London, vol. 33, 1878, p. 281. * Roberts : Ann. ch. et phys., 5th series, vol. 13, 1878, p. IIL w Violle: C. R., vol. »>, 1877, p. 543; vol. 87, 1878, p. 981 : vol. 89, 1879, p. 702. (693) 40 MEASUREMENT OF HIGH TEMPERATURES. made the basis of measarement. Both methods give the same resnlt. The thermal comparisous are based on the porcelain air-thermometer of Deville and Troost. Furthermore, Erhard and ScherteP at about this time made elaborate re-determinations of the melting points of very ])ure Prinsep's and other precious alloys, by simultaneously exposing these alloys and a porcelain air-thermometer in a large mnf9e. Having obtained a series of silver-gold and gold-platinum alloys, melting be- tween 984^ and 1,408^, they apply these data practically, determining by means of them a table of melting points of known silicates (1,208^ to 1 ,4440). Conechy,' at the suggestion of Garnelley, used fusing points to find the temperature at which arsenic volatilizes. Silicious mixtures of gradually increasing fusing points have been investigated by Seger, ^n Germany, and his tables are printed in full by Lauth,^ who also gives some attention to alloy fusions. Seger's mixtures are made of feldspar, chalk, and kaolin, substances easily obtained, and they fuse between 1, 1000 and 1,7000. Finally, the data of Le Ohatelier^ must be mentioned, by whom fusing points, as well as temperatures of chemical decompo- sition, have been measured. Tables of melting pointe are published in great fullness by Garnelley.^ Excellent and serviceable tables of this kind are also to be found m Landolt and Boernstein's® Physikalisch- chemische Tabellen. Specific heat^The measurements of temperature calorimetrically dates as far back as Guyton-Morveau,^ in whose pyrometric researches it is definitely proposed. Schwarz^ used both iron and water as well as platinum and mercury. Coulomb,* in studying the relation between hardness and permanent magnetization, determined the temperatures before quenching or annealing, by submerging the rods in water under known conditions. Clement and Desormes^^ use iron and water for tech- nological temperature measurement, as was proposed also by others.^^ In general, however, neither is any attention given to the variation of specific heat and temperature, nor is allowance made for errors by radiation. ^ Erhard n. Schertcl : Jahrbuch fUr das Berg n. Htltten-wesen im Konigr. Sachseo, 1879, p. 154. •Conechy: Chem. News, London, vol. 41, 1880, p. 189. 3Lauth: Ball. 80c. chim., Paris, vol. 46, 1886, p. 786. *LeChatelier: Ibid., vol.47, 1887, p. 300. '^Thomas Carnelley: Meltiof; and boiling point tables; London, Harrison & Sons, two vols., 1885. ^ Landolt n. Bornstein : Physikalisch-nhemische Tabellen, Berlin, Jnlins Springer, 1883. 7 Gayton-Morvean : Ann. oh. et phys., vol. 46, 1803, p. 276; vol. 73, 1810, p. 254; vol. 74, 1810, pp. 18, 129 ; vol. 90, 1814, pp. 113, 225. «8cliwarz: Boll. Soc. Mulhause, 1827,* p. 22; Pogg. Ann., vol. 14, 1828, p. 530. 'Conlomb: Pogg. Ann., vol. 14, 1828, p. 530. »o Clement and Desormes: Dingler's Jonr., vol. 33, 1829, p. 145. " Anonymous: Pogg. Ann. 2d series vol. 39, 1836, p. 518. (694) BABU8.) METHODS OF PYROMETRY. 41 At this point Pouillet* took up these researches. He measured the specific heat of platinam between 0^ and l,200o, by direct comparisons with his platinum air-thermometer. The data found were so nearly constant as to give the calorimetric method of temperature measure- ment considerable importance. After a scientiiic basis had thus been given, the method was soon practically developed and many special forms of application were devised. Miller^ describes an apparatus in which iron or platinum is quenched in mercury. This apparatus is discussed by Schubarth.^ In an apparatus due to Wilson,^ platinum or even clay is cooled in water. Schinz^ recommends platinum and water. SiemensV diita are based on calorimetric measurements with copper and water. Bystrom^ describes a platinum water pyrometer. Weinhold,^ who reinvestigated the specific heat of platinum at high temperatures, found an anomalous behavior, while that ot iron was quite regular. From these results for iron Schneider^ calculated an extensive table. In view of the known anomalous behavior of iron at red heat, the regular variation of its specific heat, as compared with that of platinum, is certainly very remarkable, and quite at variance with more recent results of Pionchon (see below). Salleron's^** pyrometer makes use of copper cooled in water. Special attention is to be given to Carnelley and Williams's" calorimetric work, in view of the many valuable data which these observers deduce by means of it. In their experiment a platinum vessel of special form is heated to the unknown temperature and then quencheil in water. Fischer's** calorimeter again is adapted to furnace uses — cooling in water. Hobson*^ and, more thoroughly, Bnwibury,'* endeavored to apply a new method of calorimetric pyrome- try. They cool the hot air of the blast with a known amount of cold air and measure the resultin^^ temperature. Thereupon Violle** began to publish the researches to which refer- ence has already been made. By investigating formulated relations ' PonUlet: C. R., vol. 3, 1836, p. 782. 2 Miller : New Philos. Jour. Edinburgh, vol. 44, 1848, p. 120 ; Dingler^s Jour., vol. lOH, 1848; p. 115. 3 Schnbarth : Din^ler's Jour., vol. 110, 1848, p. 32. * Wilson: Philos. Mag., London, 4th series, vol.4, 1852, p. 157; Dingler's Jour., vol. 158, 1860, p. 108. *Schinz: Warme-messkunst, 1858, p. 53. <» Siemens: Diugler's Jour., vol.217, 1875, p. 291. ^ Bystroni : Mechanics* Jour., 2d series, vol. 8, 1862, p. 15 ; Fortschritte d. physik, 1862, p.:M4; ibid., 1863, p. 355. »'Weiuhold: Pogg. Ann., vol.149, 1873, p. 186. •Schneider: Zeitschr. des Veroins Deutscher Ingen., 1875, p. 16. »oSalleron : Sci. Am., 1875, p. 50. ''Carnelley and Williams: Jour. Chem. Soc. London, vol. 1, 1870, p. 489. "Fischer: Diugler's Jour., vol.225, 1877, p.4<57. i^Hobson: Ibid., vol.222, 1876, p. 40. '< Bradbury: Ibid., vol. 22:^, 1877, p. 620. »»Violle: C. R., vol. a% 1877, p. 543; Philos. Mng. Lond., 5th scries, vol. 4, 1H77, p. 318; C. R., vol. 87, 1878, p. 981 ; Ibid., vol. 89, 1879, p. 702. (Gl)5) 42 MEASUREMENT OP HIGH TEMPERATURES. between specific heat and temperature almost as far as 2,000^, he made silver, gold, copper, palladiam, platinum, and perhaps iridium, availa- ble for thermal measurement. V. Meyer* before adopting Craft's sug- gestion had measured his temperatures calorimetrically. In America, practical calorimetric temperature measurement was studied with much success by Hoadley,^ who describes an apparatus and the precautions to be observed. Like Violle, he endeavors to arrive at the melting jpoint of platinum, and finds a small value of about 1,600 C. Mr. Hoadley, however, questions the purity of his platinum. An elaborate research published by Ehrhardt^ proposes to find the specific heat of iodides, bromides, and chlorides throughout large ranges of tempera- ture. Ehrhardt measures his temperatures with the porcelain air-ther- mometer and carries his iuvestigations as far as 600^. Finally, I desire to advert to an important research by Pionchon/ This observer makes a special study of the specific heat of iron between 0^ and 1,000^, and finds a regular cubical formula to obtain between 0^ and 655^. Between 600^ and 723^ the increase is much more rapid, and between 723^ and 1,000<=> the relation is nearly linear. This inter- esting result adds a new anomaly to the behavior of iron at red heat, for in the last mentioned interval (7230-1,0000) the specific heat of iron is nearly double that which holds for the first interval^ Ebullition, — Eeference to high temperature boiling points has already been made in the sections on air thermometry. Full data are given in the tables of Garnelley and of Landolt u. BcBrnstein, just mentioned. In this place I desire to call attention to the data of Grafts,^ in which, by using napthaline and benzophenol, temi)eratures of ebullition between MOO and 350O are obtainable by the mere variation of pressure from 8.7"" to 230^"". Heat conduction. — A simple device for a thermostat is made by Jourdes^ who inserts a bar of metal into the furnace and measures the temperatures at points cold enough for the mercury thermometer. Heat is conveyed along the bar by conduction, and there are cavities to re- ceive the thermometers. A somewhat different attempt of this kind is due to Main,^ who surrounds a mercury thermometer bulb with asbes- tos and exposes it for stated lengths of time. Very elaborate attempts to determine the temperature on the inner surface of a furnace wall, by measuring the temperature of the outer surface under known conditions of conductivity, were published by Schinz.® Following a method origi- » Meyer: Berl. Ber., vol. 12, 1879, p. 1426. ^ Hoadley : Jour. Franklin Inst., 3d series, voL 84, 1882. 3 Ehrhardt: Wied. Ann., vol. 24, 1885, p. 215. -•Pionchon: C. R., vol. 102, 1886, p. 1454. 6 Crafts: Nature, vol. 26, 1882, p. 466. « Jourdes: C. R., vol. 51, 1860, p. 68; Dingler's Jour., vol. 157, 1860, p. 151. 7 Main : Ibid., vol 221, 1876, p. 117. « Schinz : Dingler's Jour., vol. 163, 1862, p. 321 ; ibid, vol. 177, 1865, p. 85. (696) baw».) methods op pyrometry. 43 i nally devised by Peclet,^ Schinz first made a namber of measurements of the heat conductivity of the material composing the furnace walls, devising special apparatus for that purpose. Having duly tested the method, however, he abandoned it because of the irregularity of the conduction phenomenon within the walls and because of its want of sensitiveness as compared with electric methods. All the above methods have failed in practice. On the other hand^ the circulating water-pyrometer due to Boulier* and others, in which the heat passing by conduction into the explorer or measuring part of the instrument is carried off by a current of water flowing between known levels, seems to be gaining in favor. The thermal estimate is made by measuring the temperature of the water before entering and after leaving the furnace. The indications are, of course, wholly em- piric. In Soulier's compact and ingenious apparatus the explorer is a cylindrical box, with internal cylindrical partitions so adjusted as to secure a flow of water in cylindrical sheets. Water enters the outer compartment and leaves the inner, thus avoiding loss by radiation. Accordingto Brown (loc. cit.) these apparatus, which are used with great success in connection with porcelain furnaces (Lauth), are due to Sain- tignon. Gamelley prefers a spiral explorer. Radiation, — I have mentioned that the first 4;emperature scale pro- posed was that of Newton' (1701) derived immediately from his law of cooling. A piece of red hot iron was experimented upon. Long after this M'Sweeney^ proposed to catch the heat radiated from a furnace by a concave mirror, at the focus of which he placed a thermometer. Fol- lowing close upon GoviV photometric comparison of spectra, Becquerel* published his large memoir on high temperature pyrometry. Using the red copper glass, he investigates an exponential relation in which the photometric intensity of red light is expressed in terms of the tempera- ture of the source of radiation. Oreeu and blue glasses were also used. In addition to many results which must be omitted here, Becquerel proves that although all bodies have not the same power of radiation, truly opaque bodies like platinum, lime, magnesia, carbon, differ but little in this respect as far as the melting point of platinum. Oxdiz- able substances like iron and copper are not superficially opaque when covered by layers of oxide. Exterpolating by aid of his equation Bec- querel finally concludes the 2,100^ is probably the highest temperature electrically obtainable. The identity of emissive power accepted for * Peclet : Traitd <51^n:ent. de Physique, 4th ed., vol. 1, 1847, p. 418. 3 C. F. Amagat : C. R., vol. 97, 1883. p. 1053 ; Lauth : Bull. Soc.chimique Paris, n. s., vol. 40, 1883, p. 108 ; Carnelley : Jour. Chem. Soc.London, vol. 45, 1684, p. 237; Lauth: Bull. 8oc. chimique, Paris, vol. 46, 1886, p. 786, and others. 'Newtou : Scala graduum caloris; Philos. Traus., vol. 22, 1701, p. 824. ^M'Sweeny: Pogg. Ann., vol. 14, 1828, p. 531. *Govi: C. R., vol. 50, 1860, p. 156. •Becquerel: C. R., vol. 55, 1862, p. 826; Ann. ch. et phys., 3d series, vol. 68, 1863, p. 49. Also Draper: Fundamental researches, Philos. Mag., vol. 30, 1847, p. S45. (697) 44 MEASUREMENT OF HIGH TEMPERATURES. opa<]ue bodies by Becqnerel,* involved him in a dispute with dela Pro- vostaye* in which, however, the iK)sitiou of the former was not seriously impugned. Decharme, repeating Pouillet's experiments, concludes that the inten- sity of the glow of metals, particularly of platinum, is largely dependent on the thickness of the wire. After this Crova ^ undertook a long series of experiments, in the course of which he made the subject of radiation pyrometry* practically his own. The law of emission being known, temperature may at once be measured spectro-photometrically. Crova in some of his experiments obtains his radiation directly from the bulb of a porcelain air thermometer. His results confirm Becqnerel's datum that the emissive power of absolutely opaque bodies is the samA. A series of experiments on radiation and temperature was published by !Nichols,^ who also uses his own results for a critical discussion of the work of Crova (1. c.) and of the indications of the radiation pyrometer in general. In the same year Stefan^ published his law of radiation, according to which the amount of heat emitted by a hot body in vacuo increases as the fourth power of its absolute temperature. ViolleJ using Gray^s and Trannin's photometer, determined the photometric intensity of light emitted by glowing platinum at different tempera- tures, results which he endeavors to formulate. Similar experiments he subsequently makes for silver nearly at its melting point. An ex- periment with reference to temperature and incandescence was pub- lished by Bezold.® To put the law proposed by Stefan (1. c.) to a prac- tical test, Schneebeli^ commenced a series of experiments in which ther- mal measurements between 400^ and 1,200^ were made by a porcelain air thermometer of Schneebeli's *° own construction. Radiation measure- ments are miule by a crude bolometer " of tin foil, the instrument which Langley^^ has carried to a remarkable degree of perfection. Schneo- ' Becquerel : C. R., vol. r>7, 1863, p. 681; Auiialeschimie, 4th series, vol. 1, 1864, p. 120. «D© la Provostaye: C. R. vol. 57, 1863, p. 637; Ibid., p. 1022. The older papers of de la Provostaye et Dessains; see AQn.,de eh. et phys., 3d series, vol. 12, 1844, p. 129; Ibid., vol. 16, 1846, p. 337; ibid., vol. 22, 1848, p. 358; also do la Provostaye: Ibid., vol. 67, 1863, p. 1. DuloDg and Potit's older radiation \t'ork is given in Ann. oh., 2d series, vol. 7, 1817, pp. 113, 225. » Crova: C. R., vol. 87, 1878, pp. 322, 979 ; C. R., vol. 90, 1880, p. 252 ; Ann. chim. et phys., 5th series, vol. 19, 1880, p, 472 ; Jour, de phys., vol. 8, 1879, p. 196. ^Regarding spec trophome trie work upon which measurement like the present largely depends, see Govi : C. R., vol. 50, 1860, p. 156; Trannin, Jour.de phys., Paris, vol. 5, 1876, p. 297 ; Vierordt: Pogg. Ann., vol. 1, 37, 1869, p. 200 ; Glan : Wied. Ann., vol. 1, 1877, p. 351. » Nichols: Am. Jour.Sci., 3d series, vol. 18. 1879, p. 446; ibid., vol. 19, 1880, p. 42. •Stefan : Wien. Ber., vol. 79, 2d series, 1879, p. .391. T Violle : C. R., vol. 92, 1881, p. 866, 1204 ; C. R., vol. 96, 1863, p. 1033. »Bezold: Wied. Ann., vol. 21, 1884, p. 175. ^Schnoebeli: Wied. Ann., vol. 22, 1884, p. 430. ^oSchneebeli: Arch. 8ci., phys. et nat., Geneva, vol.8, 1882, p. 244. "Svanborg: Pogg. Ann., vol.84, 1851, p. 411. "Langley: Am. Jour., 3d ser., vol. 21, KSHl.p. 187. (098) BABUB.1 METHODS OP PYEOMETEY. 45 beli finds that the law of Stefan very closely interprets his experi- ments. In a series of beautifal experiments Schleiermaclier ' puts the same law to a rigorous test. He heats a platinum wire to iucandes* cence in an inclosure, the walls of which can be heated to didereut constant temperatures (Qo to 200<=^), and from which all air has been carefully exhausted. The actual temperature of the wire is calculated from its resistance, a series of subsidiary researches in which the wire is compared with the porcelain air thermometer having previously been made. The amount of heat generated in the wire following from Joule's law, Schleiermacher has^the data necessary to test Stefan's law. In this way he proves that the heat emitted from platinum, covered or not with copper oxide, increases with temperature in greater rate than Stefan's law predicts. Schleiermacher then interprets the discrepan- cies observed. At the close of the present paragraph a few references to the use of the radiation pyrometer for evaluating solar temperature and others of great iuU'nsity is in place. Passing over the earlier measurements we find a paper of Soret,* and at about the same time one by VioUe.' The latter's memoir is particularly complete, containing the history of the subject and a discussion of methods and apparatus. Making his observations on Mount Blanc, Yiolle finds 2,50(P for the surface tem- l>eratnre of the sun. After this, observations on the temperature of flames, of the electric arc, and of the sun, were published by Bossetti.^ Using a thermoconple, he investigates a law of radiation as far as the boiling point of mercury, which law he carefully formulates. With due allowance for atmospheric absorption, Bossetti finds 9,9G5<^ as the sun's surface temperature. The process is, of course, one of extrapola- tion. The same method applied to the temperature of the electric arc gives 2,6000 and 3,900^ as the temperatures of the negative and posi- tive poles respectively. A further important contribution to solar sur- face temperatures is due to Crova.* Other optic methods of pyrometry^ endeavor to establish the rela- tions between temperature and the character of the spectrum. Dewar and Gladstone^ attempted and finally abandoned a project of this kind. On the other hand, however, Stas' refers with some enthusiam to the » Schleiermacher : Wied. Ann., vol.26, 1885, p. 287. -Soret: Ann. do Piccolo norm, supdr., 2d series, vol. 3, 1674, p. 435. ' Violle: Ann. ch. et pliys., Paris, vol. 10, 1877^ p. 289. ^Rossotti : Ann. cb. et phys., vol. 17, p. 177, 1879 ; C. R., vol. 89, 1879, pp. 384, 781 ; Philos.«Mag., London, 5tb series, vol. 8, 1879, p. 324. fiCrova: C. R., vol. 95, 1882, p. 1271. •Prof. Cleveland Abbe has called my attention to a piiper in the Comptcs Rendns, in which the continuous change of rotation of the plane of polarization of quartz, with temperature, is made the basis of thermal measurement. Unfortunately I can not now supply the reference. 'Dewar and Qladstone: Chemical News, vol. 28, 1873, p. 174. "Stas: Bull. Acad. Roy. Belgiqne, 3d scries, vol. 7, 1884, p. 290. (699) 46 MEASUREMENT OF UIGH TEMPERATURES. research of Fievez,^ in which the attempt to associatid the wave-length character of the spectrum with the tem^ieratare of the source has a^in been made. Becently a namber of German physicists have undertaken a re-interpretation of Draper's law. I have only space to allude to the papers of H. F. Weber,* Stenger,^ and Kovesligethy,* by whom the questions relating to emission and absorption of light are being vigor- ously discussed. In America a series of well-known researches have been published by Laugley.^ Having perfected the l>olometer, and thus developed a new method for the measurement of radiant heat and light, Laugley, in a series of researches which' are still in progress, has determined the distribution of energy in prismatic solar spectra and in the spectrum of the grating. Proceeding thence to artificially incan- descent bodies, Langley is actively engaged in mapping out the char- acter of their spectra for all temperature Oo to 2,000o of the source. Less adapted for accurate measurement are certain pyrognomic sab- stances^ which discolor with temperature, such as the iodides of copper and mercury, for instance. To this class belong the oxide coats^ which form on iron and copper. The tints, however, depend not only on the temperature but very materially on the time of exposure.' Viscosity. — Very little use has been made of the viscous qualities of a substance for temperature measurement. Sir William Thomson,^ indeed, proposed a thermoscope based on the change of viscosity of liquids, more especially of water with temperature; but it is intended for low temperatures, and does not seem ever to have been used. In my own work I have found that kaolins and fire clays could be classified by noting the amount of sag at a given temperature and for a given time, which rods of the same form and dimensions experienced wlien spanning the distance between supports at a given length apart. The criterion here is flexural viscosity. Such a process would lend itself for temperature measurement conducted in a way similar to the fusion experiments in the case of alloys. It seems curious, however, that no attempt has yet been made to base pyrometric measurements on the viscosity. of gases. Following Maxwell's^® well-known investi- gation, the viscosity of gases is independent of the pressure and de- pendent only on the absolute temperature. From a theoretic point of view, therefore, such pyrometers have almost as much in their favor as * Fiovez : Bull. Acad. Roy. Belgique, 3d series, vol. 7, 1884, p. 348. ^H. F. Wober: Wied. Anu.. vol. 3i}, 1&S7, p. 256. 3Steuger; Ibid., 1887, p. 271. * * Kovesligethy : Wied. Ann., vol. 32, 18S7, p. 699. *LaDgley : Aiu. Jouru. Sci., 3d scries, vol. 25, 1883, p. 169. « Hess : Dingl. Jour., vol. 218, 1875, p. 1^.\. 'Fischer: Dingler's Jonr., vol. 22r>, ls77, p. *J78. *Barii8 & Strouhal: Bull. U. S. (Jcol. Survey, No. 18. ^•Thomsou: Proc. Royal Soc, E«linbnrgli, vol. 10, 1880, ]>. 537. »« Maxwell: Pbilos. Mag., Loudon, 4th Meritv, vol. 19, 1860, p. 19; ibid., vol. 32, 1866, p. 390; ibid., vol. 35, 1868, pp. 129, 185; Phi los. Trans., vol. 1, 1866, p. 249. (700) BABUB.] METHODS OF PYROMETBT. 47 the air thermometer itself. The form of apparatus most easily used experimentally, viz, the platinam trauspiration tabe, is based ou prin- ciples not quite as direct as Maxwell's law. Nevertheless Meyer* has BQCceeded in interpreting GrahamV data, has discussed his experi- mental methods, and has more recently shown that both Graham's and Coulomb's vibration methods lead to the same results. Work of this kind has also occupied Stefan.^ In Meyer's deduction the volume of gas transpiring per unit of time under given conditions, besides de- pending on the pressures, the internal friction, the length of tube, involves an expression containing the fourth power of the radius of the capillary tube and the ratio of internal to external gaseous friction coefficiented by the third power of radius. Hence jn such a pyrometer the coefficient of heat expansion of platinufn must be some- what carefidly predetermined. According to Nichols (1. c.) this is by no means seriously difficult. Supposing a capillary platinum spiral to terminate in two larger platinum tubes (of which one may wholly en- velop the other), we have given at once the effective part of the mech- anism of a thermometer based on the viscosity of gases. Such a ther- mometer may be used as far as the melting point of platinum. For temperatures beyond this, porous fire-clay plugs in an impervious tube suggest themselves. Acoustics. — ^The next year after Pouillet's fundamental research on pyrometry, his brilliant and ingenious countryman, Cagniard-Latour,* acting In concert with Demonferrand, proposed an acoustic air ther- mometer. Inasmuch as the velocity of sound in dry air is proportional to the square root of the absolute temperature, Latour and Demonfer- rand easily wrought out a formula in which temperature is expressed in terms of the vibrations of the fundamental note of their apparatus at the high temperatures and at normal temperatures. They estimate that the error of a comma would not exceed 30^ at l,000o. This apparatus was afterwards reinvented by Mayer,* who discusses its principle ex- haustively. Mayer calculates tables for temperature, velocity of sound and wave length, between — 300^ and +2,000o, and suggests many devices of measurement After Mayer the same principle was empha- sized, by Ghautard,® who simplified the apparatus necessary, but he expresses some doubt as to its efficiency. » O. E. Meyer: Fogg. Ann., vol. 127, 1866, pp. 253, 353 ; ibi.d., vol. 125, 1865, pp. 177, 401; ibid., voL 143, 1871, p. 14; Wied. Ann., vol. 32, 1887, p. 642; cf. Konig, ibid., p. 193. • * Graham's original researches. See Philos. Trans., London, 1846, p. 573; 1849, pt.2, p. 349. The suggestion of using platinum capillary tubes at high temperatures is my own. •Stefan: Wien. Ber., vol. 46, 1862, p. 495. * Cagniard-Latour et Demonferrand : C. R., vol. 4, 1837, p. 28. •Mayer: Pogg. Ann., vol. 148, 1873, p. 287. •Chautard: C. R., vol. 78, 1874, p. 128; Pogg. Ann., vol. 153, 1874, p. 158. (701) 48 MEASUREMENT OF HIGH TEMPERATUKE8. ThermO'eUctrics, — Tbe use of the thermo-couple for high temperature j)yrometry was su^rgested and carried to a high state of perfection iu the great research of Pouillet.^ Ue used irou and platiuum for his coujile. Subsequent observers suggested a wide range of substances for the purpose, and improved the methods of electrical measurement and thermal comparison, the best of them, however, following very closely in the footsteps of Pouillet's research. Solly* proposed an iron-copper couple, without, however, attempting to calibrate it Regnault' tested an iron-platinum element but failed to obtain satisfactory results. This unfavorable dictum of the great experimentalist is much to be regretted, for it was probably the main reason which threw tUe subject of'thermo- electric pyrometry into undeserved disrepute. Fortunately Becquerel* resuscitated the method, and in his hands it led to the new results cited above. Becquerel's elements were of platinum and palladium, of two different kinds of platinum, and of x)latinum and iron, among which he preferred the former. After Becquerel, Schinz' began thermo-elec- tric pyrometry with great vigor and success, and it is indeed curious that Schinz's work is so little known. His iron air thermometer, adapted specially for calibration work, has been already described. Its chief merit is this, that an irou tube closed within, projects from the base of the cylindrical bulb into the interior. This tube, being co-axial with the stem of the bulb and the bulb itself, serves for the introduc- tion of the thermo-couple, the junction of which may thus be ejiposed at the center of figure of the bulb. The re-entrant form of bulb, to which I myself was led in my experiments quite independently of the almost unknown paper of Schinz, I regard essential to accurate and expeditious calibration work. Deville and Troost*^ condemned bulbs of any other than spherical form, though, it seems to me, quite unjustly and without sufficient evidence against them. In thermo-electric comparisons the chief end iu view is to secure identical conditions of exposure for the junction of the couple and the bulb of the thermometer; for the errors which result if this identity does not obtain, are apt to be much more serious than such as are due to small irregularities of contraction of the bulb. It does not seem proven, moreover, that a bulb will not contract regularly if its form is not spherical. Schinz's bulb is a large iron box^ with which fine measurements can not possibly be made. The appa- ratus, moreover, is not at all adapted to the comparison of results ob- tained with different bulbs, a step which I regard as essential. My bulbs are of porcelain; they may be easily handled and exchanged one for an- other, and the whole method of exposure is such as to secure as umch iPouillet: C. R., vol. 3, 18:^6, p. 782; Dinglcr's Jour., vt.l. 03, 1837, p. 221. 'Solly : Pbilos. Mag., Loudon, 3d scries, vol. 19, 1841, p. 391. "Regiiault : Relation des Expori«nce8, vol. 1, Parih, 1847, j). 246 (1845). ^Beohy«., ^3d series, vol. 68, 1863, p. 49. '•Schinz: Dinglei-'s Jour., vol. 175, 1865, p. 87; Ibid., vol. 179, 1866, p. 436. ^^Devillo et Troost: C. R., vol. 57, 1863, p. 897. ■ (702) BABU8.1 METHODS OP PYEOMETBY. 49 facility of mainpulation as is compatible with the character of the ex- periment. My object has been to place the calibration problem within the reach of the laboratory not specially equipped for high temperature work, and thougb I have worked independently, I am glad to defer the priority of principle to Schinz. In addition to his air thermometer Schiuz invented a torsion galvanometer on the principle of Coulomb's torsion balance, for the measurement of thermo currents. This instru- ment also does credit to his experimental sagacity. His couple is iron-platinum, having failed to obtain reliable data with BecquerePs platinum-palladium couple. Schinz does not give any absolute data, and it is easily seen that the absolute value of results with his bulb could not lay claim to accuracy. He fails, for instance, to discern the iron anomalies of which Tait^ f>ub»equently made considerable study. Tait^s memoir is well known. Following the suggestion of Thomson,^ Tait makes an elaborate survey of the diagram by which the thermo- electrics of metals generally are to be expressed. For the measure- ment of temperature Tait uses a thermo-couple of platinum and plati- uum-iridium alloy, and, so far as I have been able to find, his researches are the first in which the pyrometric use of the platinum iridium alloy is recorded. I may add here that special attention to the platinum- iridium alloys seems first to have been given by Deville and Debray,^ to whom we owe so much of the metallurgy of the platinum group. A special study of the thermoelectrics of platinum-iridium and other alloys is due to Knott and MacGregor/ Diagrams are investigated for these alloys, applying between 45^ and 400^, and for compositions as high as 20 per cent, of iridium. They also study silver-palladium, iron- gold, and platinum-silver alloys with the same ends in view. In a late research Knott, MacOregor, and Smith^ determine the thermo- electrics of cobalt. Having studied the platinum-iridium alloy calori- metrically, Le Chatelier^ suggests the occurrence of an allotropic modi- fication of the alloy above red heat, the behavior being the same as that shown by iron at about 700o, and between the melting points of silver and gold. Furthermore, with the object of checking the formulsd of Avenarius^ and Tait,* Le Chatelier^ avails himself of the fusing points of Yiolle. It appears that these formulsB apply up to a certain tempera- ture, above which (** brusquement") a second formula with new constants is applicable. Platinum, platinum alloys of iridium, copper and rho- iTait: Trans. Royal Soc. Edinburirh, vol. 27, 1872-'73, p. 125. ^Thomson: Philos. Trans., London, vol. 146, 1856, p. 649. 3 Deville et Debray : C. R., vol. 81, 1875, p. 839 ; Cf. Ann. ch. et phys., 3d series, vol. 56, 1859, pp. 431 (iridium), 415 (rhodium). < Knott and MacQregor: Trans. Royal Soc. Edinburgh, vol. 28, 1876-77, p. 321. »K., M., and 8. : Proc. Royal Soc. Edinburgh, vol. 9, 1876-77, p. 421. "Le Chatelier: Boll. Soo. chiniique, Paris, vol. 45, 1886, p. 482. ^Avenarius: Pogg. Ann., vol. 119. 1863, p. 406; Ibid., vol. 149, 1673, p. 372. •Tait : Trans. Royal Soc. Edinburgh, vol. 27, 1872-73, p. 125. »Le Chatelier: C. R., vol. 102, 18S6, p. 819. Bull. 54 4 (703) 50 MEASUREMENT OF HIGH TEMPEBATUBES. diam, ami palladium are tested, and he finds that high temperatore measuremeuts thermo electrically made can be relied upon to 2(P. ^^11 r^sulte de mes recherohes," adds he, ^* que la loi d'Aveuarins et Tait continue ^ se verifier au-dessns de 40(P avec une approximation 6gale k celle qu'elle comporte audessous, jnsq'^ une certaine temperature limite, variable avec la nature des couples consider^." The superior- ity of the platinum-rhodium couple^ of Le Ghatelier's (which is his special contribution to thermoelectric pyrometry) over the iron platinum or platin-palladium couples is due to greater homogeneity of the former, and the fusing point calibration may be considered accurate within 5^ C. In a very full paper recently published, Le Ghatelier* shows that the condemnation which was inflicted on Pouillet and BecqnerePs methods was thoroughly unjust Believing the fusing and boiling point method of calibration to be superior to direct comparison with the air thermometer, he selects the series, HjO (lOOO), Pb<3230), Hg (3580), Zn (4150), S (4480), Se (6650) Ag (9450), Au (1045o), On (10j4O), Pd (loOOo), Pt (17750), most of which values are due to Violle (1. c). Having, moreover, given attention to the errors due to homogeneity Le Chatelier concludes with Becquerel,^and many others^ before hiuu that to make the AvenariusTait formula sufficiently applicable it is uec*^8- 8;iry either to add a cubical term or else to use two laws, one for low and the other for high temperatures. In a final memoir Le Chatelier^ invents an ingenious method for fusing point measurement, and compares his results with those of Oarnelley (1. c.)- The table given contains data for alkaline and metallic chlorides, cast-irons, nickle, etc, and the ] taper ends with an investigation of the temi>erature of chemical phenomena ill which heat is absorbed or disengaged, or in which the substances undergo transformation. Finally, I desire to add that the thermoelectric effect of changes of physical state and of molecular changes in general, has not been left unnoticed. Obermayer'b® experiments largely refer to alloys which melt at comparatively low temperatures. Tidblom'^ investigates an amplified form of the thermo- electric equation, in which changes of the kiud iij question may be allowed for. Electrical conductivity. — The measurement of temperature in terms of electrical conductivity was not attempted at so early a date as the thermoelectric methods. Miiller^ attempted to co-ordinate tem^iera- tnre and resistance both for iron and for platinum, without, however, more than estimating the thermal datum. A resistance thermometer, * Le Chatelier: Boll. Soc. chimiqiio, Paris, n. a., vol. 47, 18d7, p. 2. *Le Chatelier: Jour, do physique, vol. 6, lb87, p. 23. ^Becquerel: Ann. ch. et phys., Paris, 3d series, vol. 68, 1863, p. 49. *Cf. Mousson : Physik, Ziirich, 2d ed., vol. 3, 1874, p. 384. '^Lo Chatelier: Bull. Soc. chimiqne, Paris, n. s., vol. 47, 1887, p. 300. « Obermayor : Wien. Ber., vol. 66, pt. 2, 1872, p. 63. ^Tirlhlom : Beibl., vol. 1, 1877, p. 151. «MUller : Fogg. Ann., vol. 103, ia>8, p. 176 (704) BABUfl] METHODS OP PYROMETRY. 51 suggested by Quincke, was carried oftt practically by Beissig.^ This is simply a wheatstone-bridge adjustment, not different in any essential respect from C. W. Siemeus's^ pyrometer, except in so far as the latter endeavored to calibrate his electrical a[)paratns by the calorimetric method. Siemens's pyrometer is too well known to need special descrip- tion. In the final form, currents are measured electrolytically, and to give the method greater sensitiveness two identical voltameters to cor- respond to the hot and the cold wires are used simultaneoi\sly. This makes the apparatus to some extent independent of the local and time errors of the galvanometer. Siemens's resistance-temperature measure- ments are made with platinum, copper, and iron, and the data obtained are formulated. Siemens's pyrometers were tested by Weinhold (1. c.) and pronounced sufficiently in keeping with the air thermometer to be of reliable serv- ice to the metallurgist. After this Forster,^ Williamsen,* and Fischer* find that the effect of long-continued exposure of a Siemens pyrometer is an increment of the resistapce of the exposed wire. Eecalibration from time to time is therefore essential. An important series of meas- urements of the relation between resistance and temperature was made for quite a number of metals by B^noit.^ His temperatures run as high as 860^ (boiling point), and all the relations are formulated. Iridio- platinum wire was tested with regard to its resistance at 15^ and at white heat by Bucknill."' Formulae applying for silver platinum, iron- gold, and platiuum-iridium alloys were computed with great care and from many experiments by MacGregpr and Knott ;^ but their ranges of temperature did not much exceed 150^. A critical comparisou of the data of the resistance temperature formula) of Siemens (1. c), Benoit (1. c), which apply for platinum, was made by Nichols,^ and the dis- crepancies between these results fully pointed out. Nichols, moreover, expressed resistance in terms of his dilatation thermometer. Perhaps one of the most careful measurements of resistance as varying with temperature, and indeed the only ones which to my knowledge were made at high temperatures and by direct comparison with the porcelain air thermometer, are due to Schleiermacher.*® This observer wrapped his wires directly around the thermometer bulb or exposed them in sim- ilar unexceptionable ways. Becoguizing the variable character of ordi- ^ Reissig: Dingler*8 Jour., vol. 171, 1864, p. 351. 2 Siemens: Proc. Royal Soc. London, vol. 19, 1871, p. 443. Dingler's Jour., vol. 198, 1870, p. 394 ; ibid., vol. 209, 1873, p. 419 ; ibid., vol. 217, 1875, p. 291. « Forster : Chemical News, vol. 30, 1874, p. 138. < Williamsen : Dingler's Jour., vol. 210, 1873, p. 176. » Fischer: Dingler's Jour., vol. 225, 1877, p. 463. «Boint8, sufficiently near together to make linear or quadratic interpolation practicable. Carnel- ley^ and others have nuule much effective use of methods of this kind. ADVANTAGES OF THERMO-ELECTRIC PYROMBTRY. Having thus indicated the chief methods of pyrometry so far em- ployed, it next behooves me to state clearly in what respect the thermos electric method deserves preference before all others. To do this I must reiterate the point of view already emphasized in the preface and from which the greater part of the present volume has been written. It is my bqlief that before important steps in most subjects directly bearing on dynamical geology can be made, our methods of high temperature measurement and of high pressure measurement must first be facilitated. Moreover, the solutions to be given to the thermal and to the mechan- ical problems must be such that the high temperatures may be measured under conditions of high pressure, and conversely. When tenipcratiue measurements are to be made under these almost ' Callendar : Proc. Royal Soc. London, vol. 41, ISSfi, p. 231. 2 Buchanan: Pliilos. Mag., London, vol. 24, 1887, p. 287. Tho siibjoct is now being vi go ron sly discussed; but there is no space for further references here, (Schuator, Blomllot, Elster n. Geitl, and others.) ^Tliomson: Proc. Koyal Soc. Edinburgh, vol. 10, 1880, p. 538. "* Cariielley : Jour. Chem. Soc. Loudon, vol. 1, 1877, p. 365. (TOG) BABUB.] METHODS OF PYROMETRY. 53 insuperable difficulties, the kinds of pyrometers available dwindle down to a very small number. Indeed, tlie thermocouple is almost the only instrument of research left. It is therefore most encouraging to find that, for purposes of high temperature measurement in geneial, the thermo-couple can be made to yield results which, apart l&om practical conveniences and easy manipulation, are warrantably as accurate a^ any known to us. I will summarize the advantages here in question as clearly as I can, so that they may be referred to in the bulk of the work : 1. Barring a few corrections, the thermo-couple of known properties is available for temperature measurement under all pressures. The cor- rections implied are those which become necessary in consequence of the changes of thermoelectric property with pressure; but these changes are slight and quite negligible in comparison with the thermal sensi- tiveness of the couples. 2. The temperature at the hot junction is dependent on the tempera- ture at the cold junction and the constants of the couple only. It is independent of the distribution of temperature in the parts of the couple between the junctions. This is a great practical advantage, the impor- tance of which is realized when temperature is to be measured under pressure. 3. The thermo couple is capable of measuring temperature when the dimensions of the hot space scarcely exceed a physical point. Small zones of constant temperature and relatively small apparatus fpr heat- ing are therefore sufficient for thermal comparisons of relatively great accuracy. In this respect the thermocouple deserves preference to the resistance thermometer, particularly when material fusible with great difficulty is operated upon. 4. The upper limit of temperature measurement is practically infinite, and lies much above the melting point of platinum ; for by using re- fractory alloys of platinum, iridium, rhodium, and inclosing wires of these metals in tubes of calcined lime, distinct and powerful thermo- electric effects are obtained even when the contents of the tubes are fused. 5. The electromotive forces of suitable thermo-couples are easily meas- urable with an accuracy of 1 in 1,000. Almost with the same accuracy may the indications observed at the beginning of any year be compared with those at the beginning of the next or any other subsequent time. The secular errors of a thermo-electric pyrometer, when properly cared for, need not be larger, relatively, than the secular errors of a mercury thermomet>er. 6. Many couples are known which, in addition to the desideratum of thermal sensitiveness, possess great tenacity and ductility, and are unalterable under ordinary conditions of heating. 7. The thermal indications are as nearly as possible instantaneous, and the discrepancy of the lag error is therefore a minimum or nil. (707) 54 MEASUREMENT OF HIGH TEMPERATURES. 8. In view of the facts sammarizcd in 2, inanlation of the wires is not difficult even w^hen the couple is to be used under pressure. This does not apply in case of the resistance thermometer. 9. When destroyed by silicification or metallic corrosion the thermo- couple may easily be purified by fusing it over again on a lime hearth and drawing to wire. With good metal the variation of constants thus produced is almost negligible. 10. Finally, the thermo-couple has this important property, that between temperatures lying not too far apart (lOOo to 200°) any inter- mediate temperature may be interpolated with great accuracy by the quadratic equation devised by Avenarius and Tait, and such interpo- lation, curiously enough, seems to be more trustworthy in proportion as temperature increases above the regions of incipient red heat. It is this property which specially recommends the thermo*couple for the meas- urement of relatively very small increments of temperature added to relatively large temperatures, possibly under conditions of high pres- sure, a^ is the case, for instance, in investigation relating to melting point and pressure of solids. To use the thermo-element it is necessary to find the thermal equiva- lent of the electromotive force for all temperatures of the junctions. This is at present possible only by making detailed comparison with the air thermometer. An experimental problem of some difficulty is thus encountered at the outset. Inasmuch as the measuring part of a thermo- couple is not much more than a sensitive point, and the corresponding part of the air thermometer is a sphere of relatively enormous dimen- sions, it is not easy to devise an environment which at temperatures high and low shall be thermally identical for both. When temperature varies, the indications of the air thermometer necessarily lag behind those of the thermo-element. It is therefore one of the chief purposes of the present volume to devise a method such that the observed indi- cations of air thermometer and theimo-element may be rigorously equiv- alent; in other words, to carry forward the methods of calibration to a degree of perfection subject only to the improvement of the air ther- mometer. 1 hope in some future publication to show the feasibility of a fire-clay air thermometer which will be available for temperature meas- urement much above those at which porcelain becomes too viscous for further use; but in much of the present volume the object is less to de- vise new methods, than to bring the old ones more within the scope of easy application than has hitherto been oint8 this apparatus is made of metal and appropriately jacketed. For high boiling points, crucibles of graphite or of clay are preferable. In the interior of the central tube and near the center of figure of the cruci- ble the temperature is satisfactorily constant. Here, therefore, is placed the essential part or '* explorer'' of the pyrometer to be calibrated. It is thus exposed in the current of vapor circulating through the tube, the walls of which are permanently kept at the boiling point by the boiling liquid surrounding them. In this way a comparatively simple form of apparatus, available at all temperatures, both high and low, Trains all the essential features of the ordinary boiling point apparatus ; and it is only for very low temperatures ( < 100^) that a special form is expedient. Low boiling points. — To describe in passing this form of apparatus for low temperatures ( < 100^), we insert Fig. 1, in which the position of the thermo-element is indicated by taT. The cold junction t is kept at constant and comparatively low temperature by water com- ing directly from the water mains and continually circulating around it« This cold water is further used in condensing the vapor after cir- culating around the hot junction T. A glance at the cut will make the disposition clear. Water enters at w and vapor at v, and after passing around the junctions t and T, respectively, they enter the con- denser, diagram matically shown at cc, the water entering an external compartment and the vapor an internal compartment. The condensed vapor is at once refed into the boiler or j9ask, thus enabling the observer to use this apparatus quite as long as desirable without inter- ruption. At the cold end of the condenser the inner tube is in commu- nication with the air. Ebullition thus takes place under atmospheric pressure. The apparatus is available for experiments with ether, methyl • alcohol, alcohol and water. It fails, so far as practical convenience is concerned, for aniline, etc., because of the difficulty encountered both in conveying the vapor into it from the boiler without condensation, and because of the corrosive action of such vapors on the corks and rub- ber tubing of the apparatus. If made of a single piece of glass it is (712) BABin.1 DEGBGE OF CONSTANT TEMPERATURE. 59 too liable to break at the fused joiDte. In tbe form used the tubes v T and wt were about 26™ loa^ and about 2^'" wide. Fhi. I. Appantm far oouMMit temparatAre between 0° Bod 100°. Soil*, 1. Boiling points between 100° and 300°. — In Pig. 2 we give a form of ap- paratus couBtructed on tlie typical plan indicated above, and whiob is adapted to temperatnre between 100° and 300°. It consists essentially of a large spbere, AAA,o{ copper, 25"" in diameter, tbe joints of which are brazed. Tbioagh the bottom of this a somewhat conical central tube, d d, pro- jects into tbe interior as shown, the tube commaaicating below with an iron gas- pipe, e/gh, loading to the condenser. Thenecit or head, k, of tbe spherical copper bottle is In connection with a wide glass tube, k m, kept in place by a gallows adjustment, the top of which, m, is of iron and provided with two lateral st«el rods or bolts. These being fastened (713) 60 MEASUREMENT OF HIGH TEBfPERAtURES below to a wide flange in the neck A?, secure the tube by screw pressure between the head m and the flange of Jc, It is often convenient to use gaskets of asbestos or any other kind of packing at the upper and lower end of the tube. The head m, moreover, is in communication with the condenser by means of the lateral tube of gas pipe, mnog. Hence the vapor arising from the surface of boiling liquid, a a, can escape either Fio. 2. Apparatus for constant temperature between 10

. Scale, V^. above or below, and the respective circulations are regulated by a faucet, /. We found, however, that in case of corrosive or hot liquid, / soon begins to leak, and that it is advantageous to partially stop up the lower passage by a ball suspended in the cone d d from' a platinum wire passing through JcmL In this way the use of the cock / may be avoided. To heat the sphere A A A we used a large ring burner, B B^ about 22*^™ in diameter and provided on its inner surface with 130 jet holes, 0.15*'"' each in diameter. This ring burner was so made that it could be used either with or without blast, according as temperatures relatively low or high were to be obtained. Its position is adjustable at pleasure by a clamp attached to the standard G C. Another clamp attached to the standard D D acts as a safeguard against lateral vibrations of the sphere AAA^ the main weight of which is supported by the exit pipe d e/ to the upper end of which it is screwed. A final clamp and stand- anl, E r, facilitates the adjustment of the exit pipe o n m. The sphere is piovided with a feed pipe, q q, and an appropriate gauge, ppj to (714) DEGBEE OF CONSTANT TEHPERATCBE. 61 register the beight of the liquid. The capacity of the retort is aboat one gallon of liquid. If the liquid be fed in drops from a Mariotte flask, JP, no interrnption of ebullition need take place. In the apparatus given in the flgare a space of constant temperatnre nearly S"" wide and fully 60"° long is^vailable. If the ring burner be so adjusted that the eballition is fairly brisk the temperatare within this spaceis almost perfectly constant. Forrelatively high temperatures it is generally advisable to discard the glass tube It m, and to close the neck with a plate of metal suitably perforated to allow the introdnctioD of thermo-couples. In general, however, the large tabalar space is con- venient both for the comparison of long-stemmed mercury tbennometers and for the further comparison of electrical pyrometers with them. We omit special data relative to the degree of constant temperature here obtained, because it is questionable whether at these relatively low temperatures the nse of large forms of vapor baths is to be recom- mended, and because none of the data of importance below depend upon the perfection of the large retort here described. In Chapter II data for smaller forms are fblly given, and iiom these the efflciency of -the larger forms may easily be iafened. Fiu. S. BolUng-poliit kppufttoi for meraorf. Soala, ^ A^aratus for fliercitry,— The boiling-point apparatus just described is useful for substances boiling at a lower temperatnre than mercury when constancy of hoiUng point can not be accurately relied upon. Such substances are mostly of organic kind, and are apt to change their properties slightly after long ebullition. It is for this reason that the mercury thermometer rijmaiiis iadi8i>ensable. When, however, the boiling point is fixed and known, like that of mercury or sulphur, the (715) 62 MEASUREMENT OF HIGH TEMPEBATURES. apparatus and the manipalations may be simpMecl. A form of vapor bath specially adapted to mercary calibrations is given in Fig. 3, one- tenth actual size. The boiler or retort A A AiB of cast-iron, and is a modified form of the well-known mercury still of the shops. By drill- ing a hole through the bottom and tapping into it a long nipple, the central tube d d may be screwed down firmly in position. The nipple communicates below with a long tube of gas pipe, efg^ leading to the condenser. The crucible A AAia closed above by a liat lid, the edge of which as well as the rim of the crucible has been carefully turned, and is held in place by a stout gallows connection not shown in the figure. Through the center of the lid passes a smaller iron tube, h tj the lower end of which is closed and projects into the central tube d dj somewhat below the level a a of the surrounding mercury. It is into the tube h t that the hot junction of the thermoelement is to be intro- duced as far as the base of the tube. A lateral tube, bJclftj largely of irou, subserves the purpose of rei)laciug the mercury lost by evapora- tion, and communicates with a larger reservoir, B B^ in which the mer- cury is practically at the same level, m w, as in A A. Hence the level in ^ ^ is to some extent a gauge of the level in A A, A supply reser- voir, C 0, enables the operator to keep m m at constant height. To keep up the ebullition we made use of a kind of ring burner, consisting of three distinct blast-burners symmetrically placed around the crucible, the flames impinging upon its sides. In this way full advantage was taken of the current of air furnished by Professor Richards's pneumatic pump. The operation of boiling may therefore be prolonged indefi- nitely. In the tables below we give a series of results by which the con- stancy of temperature attained during the successive stages of improve- ment of this apparatus is fully exhibited. These results will show that variations in the disposition of parts is by no means without conse- quence. Boiling point of zinc. — The construction of apparatus first used was carried out by Mr. Hallock, and to him the following description is due: In our earlier experiments an attempt was made to use the large clay retorts of the shops, but after some trials we abandoned them in favor of the special forms of retort now to be described. Having in mind the form and operation of the ordinary apparatus for checking the boiling points of thermometers a retort wa« constructed with a view to surrounding the thermo-element with a double jacket of the vapor in question. It soon became evident that the simpler forms were useless, owing to the condensation of the vapors and the clogging of the outlets. We were thus led after trials of several other simpler forms, to test the arrangement shown in Fig. 4 and constructed as follows : (716) «■! DEOBEE OV CONSTANT TEMPEUATUBU. (717) 64 MEASUREMENT OF HIGH TEMPEBATUBES. The cylindrical reservoir, or retort i)roper, shown at A, Fig. 4, was made by screwing cast-iron caps N Nj G Gj upon the ends of a piece of iron pipe 6 inches long and 6 inches in diameter. A piece of 1-iuch iron pipe, 2), fitted in the upper cap C, and extended upward to an elbow, U^ and similar pipe, By which latter passed out through the side wall of the anthracite furnace at O 0. Thence the pipe B extends through the T at J J, 18 inches, into the iron pipe H JJ, which is screwed into the other end of the T. The third opening of the T is fitted with the short outlet pipe K, 1 inch in diameter. A cap; G, closes the whole apparatus except the outlet at K. A small iron pipe, F Fj passing through the cap (?, and extending 15 inches into the interior tube B By and closed at its inner end was intended to receive the thermo-element. A perforated tube burner, LLLy Fletcher system, placed beneath the pipe R Hy was intended to prevent the solidification of the metal therein and consequent stoppage of the circulation of vapor. We hoped to be able with this apparatus to obtain a region of constant temi)erature in the inner end oC the tube Fy which would be surrounded by two distinct jackets of the vapor of zinc. We expected the action to be as follows : The vapor rising from the boiling zinc in the retort A, to pass through D and B By out past the end of Fy out of the end of B into H Hy thence backward through Hy and out at £, either still in the state of a vapor or condensed to a liquid in H. Two difficulties made the apparatus impracticable. Whereas melted zinc or zinc vapor has little or no solvent effect upon iron, still zinc just at the boiling surface or at the point of condensation of the vapor does dissolve iron in considerable quantities. This action of the boiling zinc soon eats through the iron walls of the retort and makes the whole ap- paratus very short lived. Moreover, the spontaneous combustion of zinc vapor on coming to the air inevitably results in stopping up the outlet, causing the destruction of the apparatus. These objections, to- gether with other minor ones, led to the abandoning of this form and ultimately of all forms constructed on a similar principle. The principle next applied was that of downward distillation through the bottom of the crucible, a system that had already proved very good for mercury and some other substances, and which has been touched upon in an earlier part of this chapter. The particular form ultimately constructed is shown in vertical cross- section in Fig. G and in vertical longitudinal section in Fig. 5. In this case the furnace formed an essential part, and was constructed simulta- neously and as part of the whole. It covered 6 x 3 J feat on the floor and stood 5 feet high. It was built of brick, lined with fire-brick, on the double-reverberatory principle, entirely symmetrical. Each side was provided with a fire-box, A (Fig. 5), a grate, O, ash-box. By ash-door, (7, blast inlet, Qy and fire-box door at D, The zinc was coatained iu the (718) BiBi-8.1 DEGBEE OF CONSTANT TEMPERATHKE. 65 graphite crucible F F, which was 14 inches high, 11 inches in largest diamtter, and f inch thick. The graphite cover Af JIf waa luted on with- a paste of powdered graphite and wat«r. Through the cofer M M the iron tube L passed, extending downward into the crucible and closed at its lower eud. An iron pipe, Q, 1^ inches in diameter, passed up through the bottom of the crucible about 6 inches, carrying the fire- clay spherical shell K K, and protected by a coating of fire-clay, II. _^-«^ ^^"^^TTT^— _ iiS \ i r~ '~~~ — — ■ — ~r^ (I ' S / = \y ^ 1 U. / "--. 1 \ I ' 1 *' ■ D M n ' r~i L pn , □5T».tW..i: L .......... o' ■ ■ ' ■ J □&«r-,:t j ■ li-^r. t 1 u ^ 1 a & I 1. \ ( 8 '' _^ 1 Fia. 5, Builm|:>poiiit fumacD Coti irform; laDRltudiual HGtlou. Scale, A- Undeme-atb the cmcible a i>i»!co of stone-ware pipe, C inches in diam- eter, N JV, was bnilt into the furnace conceutric with the crucible and extending 15 inches below it. In ]»ractiee this pipe JrA''dii)3 just below the surface of tlio water in a tank placed between the two fire-boxes A A and not shown in the drawing. Ilnll. 54 r, (719) 66 MKAyUBEMENT OF HIGH TEMPERATURES. Fig. Gsliowa a vertical section t]iroajj;U the axU of the cracible at right angles to that shoivn in Fig. 5. Tlie lettering in t'aeh case is the Sitmv. Uantl T''ariitboHui>iK)rtiris:urcb between the two fires, aod TT are flues to carry ofl' the products of combustion, if £ is the top of the furnace, S i' arc acpporting columns, W is the entrance of the blast, and P the wind-box opening into the tires by Q Q, shown on Fig. 5. FlO. e. BoUlnKpolntfuniHCBforjiinc; Inter form; ctOBiBectiun. SciUr, A- The fuel used iii this furnace was anthracite coal with a blast furnished by a 20-inch fan-blower, the ash-box door being of course closed during operation. The Jlames from tlio iiie rising through the space E E im- pinged upon the cnuiiblc and passed thenco off by the flues T T. .In practice it was found that by applying fiesh fuel in small quantities * (720) BABUB.J DEGREE OF CONSTANT TEMPERATURE. 67 alternately to the two furnaces at regalar intervals (ten minutes) a com- paratively constant condition could be maintained until the accumula- tion of ashes interfered with the draft. The furnace performed its part of the work satisfactorily, but from the large dimensions at least' one day was necessary to repair damages and prepare for a new '^heat," and sometimes several days were necessary to get the crucible cleaned and ready again. The crucible was filled with pieces of zinc and the powder and grains from previous distillirigs, mixed with powdered charcoal as a reducing agent. The cover was luted on as stated, and the tank placed under the stone pipe 2f N. In operation the vapor from the boiling metal rose around the sphere K and passed through holes into it, and down through G ixito*N' N^ where it condensed and fell into the water, thus keeping the pipe L and the thermoelement contained therein at a comparatively constant temperature. The degree of constancy actually attained will be fully discussed later. Even in this apparatus the burn- ing of the vapor proved a source of endless and unavoidable annoyance. There seems little doubt that the vapor of zinc is even able to decom- pose water vapor and liberate the hydrogen, itself producing a horn-like oxide, which is quite as apt to clog the outlets as the solid metal. Ow- ing to this, many and frequent were the ctises where the " heat" proved incomplete, or a total failure, owing to stoppages and explosions or leaks. This will account for the incomplete series of determinations which may occur in subsequent tables. Before we were able thoroughly to profit by our experience the transfer of the laboratory to Washing- ton interruuted the work and gave it a different direction. EXPERIMENTAL RESULTS. Methods of measurement, — Whether two given temperatures are equal or not may be shosvn with great accuracy and certainty b^^ thermo-elec- tric comparison. Thermo-couples of platinum with palladium, low percentage alloys of platiuumMridium, platinum-nickel, platinum-rho- dium, platinum-cobalt, and many others, are available for the purpose. Furthermore, since comparatively small increments of temperature are here to be observed, the degree of constant temperature obtained in any given space both as regards its variation at any given point with time, as well as the distribution of temperature existing in the said space at a given time, can be fairly estimated by thermo-elements of known power. Many observations go to show that for practical i)urposes we may rep- resent the j)artial electro- motive force at each junction of a thermo-ele- ment by an equation of the form er^aT+bT+cT^-^ (1) where e^is the (partial) electromotive force at the junction whose tem- perature is T, and a, 6, <•,... are therm oelectric constants rapidly decreasing in magnitude. (721) 68 MEASUREMENT OF HIGH TEMPERATUBES. Hence in a ooople in which the jauctions are at temperataroB Tand ty we find by difference e^Cr-e.^za (T-^t)+b (T^-^t^)+c {T^^f^)+ ... (2) an equation which in most cases applies so fally that the terms of the righ^haud member, whose powers of T and t are greater than the third, may be neglected. From equation (2) follows at once that Inasmnch as the constants a, &, c, . . decrease so rapidly in mag- nitude that a mean or approximate value of T may be introduced into equation (3), it appears that iu proportion as the increment of tem- perature becomes smaller it may be measured with the same accuracy with which the constants a, b, . . have been found. Methods of measuring e and of calibrating the thermoelement will be indicated in the next chapter. List of thermo-couples, — It is expedient to insert for future reference a list of the thermo-couples used for measurement here. In the first part of this table the wires are given in the order iu which their thermo- electric powers were originally determined. The other part contains the thermoelements used for temperature measurement. The table also contains values for the constants a and b iu equation (1). In the case of Nos. to 15 the calibration interval is not larger than (P to 200O ; in the others as large as Qo to 400^, or 0° to 450o. The data are referred to a zinc sulphatb Daniell standard, tlie electromotive force of which is assumed to be one volt. Lord Rayleigh's recent value for this standard is 1.072 volt. Hence to reduce the data to absolute units, a and b must be increased 7.2 per cent. ^We have refrained from intro- ducing this correction in the first two chapters because the relative values of the data there given are alone of interest, and because of the confusion and labor which a reconstruction of the whole series of data and of graphic representations would involve. (722) DEGREE OP CONSTANT TEMPERATDBE. Taui.K i.—LiKl o/tkamio-coujttit. Thnms «Bpl..- ! Ho. Inten-oL + - "7 AK Cu 174 Uboratory; d W l»o». 1 AftBftPt Cu ana l>d. B AtlO%Pt Cn 7230 loioo Do. A«.1B%P. Cn am 11830 Do. t Ag.a506Pt Cn B«l ism Do. B 4021 PtMft Cn am 12740 P»riB,o=>tol»0°. 7 Plliu^ Cn 37«0 9080 Do. P(Ii«i Cn MM Do. S Cn Pt.IrM% 33M 38S0 Do. U Pd Co BSW 21100 Do. 11 HI Cn WDM 210OO Do. Ki Ptwfl IT«B« 4W0 Do. IS Pd Ptbufd 961T 837J Do. u PtbUil Pt,Ir2l(?i 7107 0J2S Do. u Pd Co Plli«rd Pt,Irai,% Cn Pl.IrWWi IM7 108SS Do. Commereiitt : 0" to lOOo. IT 7(IS0 s»ou IB Ptbud PMrBO^ 7SU 3070 Do. IS Pi bard Ptlr a% Puu^ O°(o370°. 21 PtIlKd Pd Pt,Ir !,% Pth.nl BOM ~" Do. 11 PC hard PUr«K>i 7S40 3810 Pitrii; 0°tot(KK>. B Ptbard PNIr5"o 2072 475 P»rii.:0°toa70°. U Pthird Pt.lrS^ 1883 — ISOl u Ptwh Pt,Pd»% 2B7 not Do. 28 Pi man Pt, Pd 10% Do. S7 PI.Ii-B% Pt,lrHI% 2M2 1SZ5 Fsii,, 0O1O370'. Pt.Ir5% Pi;.IrlS% SO Pt,Ir B% Pt.Ir20% (MT 3082 pM-i.;0»to370'. 30 Pl,NlB"i BI28 MS Bl Ptoom. Pt.NlS'^ tM 48 Do. 31 Pi com. PfcNiani, Do. Ptcom. Pt.rrs% 3839 i 1472 Do. 3* Ptcom. Pt,lr-?i 4704 2073 Do. 3S PlDoft Pt,IrM% 7160 0270 P.ri.;»»l0 4»»- St pti»n PI.Irai% Do. 37 PtKft Pl.Ir»% (72001 (0300) Do. IB Ptwlt PtlrSOW (7200) (0300) FuKed over from old elomenta. S> Ptaofl Pl,trW9t (TWO) (6300) Do. « PlMlt Tl,It-X% (7200) (8300) Do. Data for tke mercury rapor baths. — Hettiniiiif; from this digrcusion to the sabject proper, we iosert Table 2 to exhibit ttie degree of constant temperature arrived at in the mercary sippaiatLii. The observations are made in time series. T is the temperature of the hot janction, placed at i in Fig. 3, and t the temperature of the cold jauction of the thermo-element So. IS, at the time specified in the s»me honzontal rov. Tis computed fkart of t^e (723) 70 MEASUREMENT OF HIGH TEMPERATURES. table, results are gWeu for the case iu which the thermoelement tube h i, Pig. 3, is simply submerged in liquid. Table 2. — Constancy of temperature in the mercury apparatus* Ko. 18 t. Time. KcTiiarkn. 5.1 4.2, 6.G 7.8 ■ ' I 9.6 ' 10.2 357 337 3J6 358 356 35f 359 h. m. 2 30 35 3 20 30 50 4 5 20 Envelope above liquid * Envelope of thernio-eleiucut (tube) submersed in.tbe boiling liquid. 18 7.2 , 359 7.2 360 2J 35 ApparatuH Fig. 3, but \\i\h longer central tube dd. Resultn irregular and usclesA ; no HUtiAfictorA* constancy. 18 15.0 17.2 342 3 40 ; f Apparatus Fig. 3, but with inner Aide of lid and walls heavily lined 357 I 4 30 ' S wiih phiater. Besnlts again irregular; no satisfactoiy constancy. 18 9.0 353.6 12 ] 10.0 357.5 10 10.8 357.5 20 11.0 357.2 30 12,0 350.0 45' 13.8 356.4 r.5 1 14.8 336.5 1 10 15.2 356.4 15 J I' Apparatus Fig. 3, with central tube projecting inward only as far UH the center of figure. Apparatus without feed-pipe. 18 6.8 7.4 8.1 9.1 10.1 11.2 354.3 10 50 356.8 11 5 356.6 , 11 30 356.7 ; 11 50 356.7 ! 12 20 356. 7 12 55 V Apparatus Fig. 3, completed form. Curiously enough, when the walls were lined with an inch coating of plaster above the plane of ebullition, although distillation took place with great rapidity, the thermo-element did,not show the boiling point until about one hour had elapsed. Where no feed-pipe is used the tem- perature gradually falls as the charge of mercury diminishes in bulk. In the final form the negligible differences of temperature, amounting (after ebullition has set in) to less than 0.2o, are probably errors of measurement. The accuracy of the thermo-electric method is not war- ranted within 0.1 per cent. Data /or the zinc vapor haths.'-lu digesting the data obtained for the variation of temperature in the zinc apparatus, it will be necessary to be more circumspect. For this reason we shall exhibit a very complete (724) BABU8.] DEGREE OF CONSTANT TEMPERATURE. 71 set of data. Early values, i. e., such as were derived with couples of palladium or of platiuum-silver alloy are discarded, because during the course of the nieasureuients such elements were usually corroded through, and little confidence could, therefore, be felt in the use of the constants of the uncorroded element. Assuming equation (1) above, the temperature, 1\ of the hot junction of the couple is ^=2".{V'+'»'-'! ■ where a and 6 are the constants of the element, and where, if f be the temperature of the cold junction and e the observed electro-motive force for temperatures t and T of the junctions This value, f, is therefore the electro-motive force when the cold junc- tion is at zero, other conditions remaining the same. The passage from 6 to £ usually involves only a small correction which may be interi>olated from tables calculated for the purpose. Nevertheless the computation of T, where many results are in hand, is exceedingly tedious; and it is therefore preferable to avoid it by the use of graphic methods, as ex- plained in Ohax)ter II. In computing the values of T, the constants obtained in later and more refined apparatus are of course used, all older calibrations being allowed no more than corroborative importance. In Table 3 we give some of our earlier results, the first of which were obtained by submerging a protected thermo-couple in boiling zinc con- tained in a large fire-clay retort. The charge was from 5 to 10 pounds, but special data are not at hand. After this the iron apparatus de- scribed in Fig. 4 was used. Owing to diflSculties of nmnipulation, we thereupon returned to the retort pattern, providing it with a suitable condenser; exchanging this, eventually, for a graphite crucible on the general plan of Fig. 5, but of much smaller dimensions. It is in this order that the results in the tables are given. The third column of the table contains the number of kilogrammes distilled and the total num- ber of kilogrammes of zinc charged ; 620 is the obs(jrved electro motive force in microvolts, nearly when the hot junction is at Tand the cold junction at 2(P ; ^20 is preferred to f, which applies for f =(P because t jn the average case is usually in the neighborhood of 20^, and therefore the correction to be added is sniall. T^ and T,„ are thermo-electric data for the boiling point, when the calibration interval within which the constants apply is respecjtively Qo to 450o and 0^ to lOOQo. T^ is therefore the result of exterpolation. Further remarks regarding these quantities must be reserved for Cliai)ter 11. (725) 72 MEASUREMENT OP HIGH TEMPERATURES. Table 3. — Constancy of tenijnraturc in earlier forms of the zinc boiling-point apparatus. Date. Apparatus. Dec. 28.1883 Jan. 10,1884 Jan. 11.1884 Jan. 16,1884 Jan. 29,1884 Jan. 30,1884 Feb. 2, 1884 Feb. 4, 1^4 Retort do Iron boiliD^-point ap]>Aratim Iletort "With couMenser Graphite iMiillng-polut apparatus. .... do do do K2. of Zn. No. of distilled ; , thcrmo- charge, couple. evt. r.. 1 1 5 ; 14 0150 847 014 14 9600 880 950 14 9C30 883 053 14 9390 867 934 18 9216 860 924 18 9184 850 921 18 9101 857 922 18 (0281) 8C5 930 It is to be borne in mind that the above data have li relative signifi- cance only. Their absolute values can not be discussed before Chapter IV. The same thermal and electric scales are uniformly used through- out Chapters I and II. In Table 4 data showing the progressive stages of temi)erature of tlie zinc crucible are given in time series. The plan is identical with that of the preceding tabh*. h denotes the number of hours elapsed from the beginning to the end of the ebullition. Table 4. — Constancy of tcniperalure in earlier forma of the zinc boiling-point apparatus; lime series. Date. Time. h. in. 4 25 h. 0.00 No. of thiTmo- couple. 18 t'vo. 9220 T.. 860 025 Keujurks. Jan. 29,1884 Charge insuflicieiit. 32 0.12 18 9180 W7 021 37 0.20 18 9170 h5G 920 48 0.38 18 9020 ^•40 910 55 0.50 18 8580 815 872 Furnace cools. Jan. 30,1884, 2 36 0.00 18 6500 658 693 Approaching; ebnllition. 45 0.17 18 7610 73G 682 3 00 0.42 18 8020 840 000 20 0.75 18 7800 756 807 Blowr-r stopped bj* acci- dent. 35 1.00 • 18 8150 781 830 40 1.08 18 8910 8:io 899 Approaching ebullition. 45 1.17 18 9150 8)4 919 50 1.25 18 0180 850 920 Ebullition. 55 1.33 18 9180 850 920 4 10 1.55 18 0260 8t)4 928 15 1.67 18 9260 804 028 30 1.02 18 0300 867 03;^ , 40 2.08 18 9370 870 938 C'har^e distilled. 50 2. 25 18 0610 F.-G 956 5 00 2. 42 18 0770 F98 970 Superheating;. 10 2. .:8 18 0080 J-OO 901 15 2.07 18 9540 882 951 Furnace c^wls. 25 2.83 18 9220 860 924 (72G) BARUB.] DEGREE OF CONSTANT TEMPERATURE. 73 Tadlk 4. — Consianoff of Umperature in earlier forma of the zinc, hoiling-point apparatus; time itei'ies — Contimu'il. Dat(>. b. 2, 1884 Time. h. No. of therm 0- \ couple. , 1 1 fto. ! i 1 1 7030 1 768 . .. 818 Ueinnrks. Fe h, fn. 3 15 0.00 i 18 1 ApproacluDg ebuUitioo. 19 0.07 18 , 8100 ' 780 833 25 0.17 18 842U 1 80*2 8C0 30 0.25 is' 8740 ; 825 884 35 0.33 18 9110 851 915 EbuUitioD. 40 0.42 18; 9170 . 85C 920 56 0.68 18 9100 8.^7 921 4 19 L07 18 I 9220 860 924 The second part of this table (Jan. 30) is complete. Tbo tliird (Feb. 2) and the first ( Jau. 20) part tOf?etlier make a series, showing in all cases the rise and fall of temperatnre at the inception and at the close of the distillation. The criterion of the occurreuce of the boiling point is con- stancy of temperature ; for the furnace is sufficiently hot to superheat the crucible when the charge of zinc is low or nearly distilled over as the second part of the table shows. An early stopping or a late begin- ning of the experiment is the result of accidents, which for the difficulty of the experiments are not infrequent. As distinguished from the above data the following results are all ob- tained with vefy large apparatus, a "number GO" graphite crucible of Messrs. Dixon, with a capacity sulficient to hold GO pounds of zinc, being used for the experiments. The apparatus and furnace have already been described and it will therefore suffice to summarize the data. This is done in the following very complete tables on a plan identical with the preceding. Table 5. — Constancy of temperature in the later form of zinc boiling-point apparatus; time scrieft. Date. Time. h. No. of : theraio- ! couple. ' i r.. 1 KoDiarks. h. m. 1 i Apr. 15, 1884 2 15 0.00 18 7980 770 Char<:o 14 pounds. 26 0.18 18 8.140 812 t-iW , 38 0.38 18 9110 ' R')2 91.-. 1 50 0.58 18 i>:.5u 882 O.VJ 53 0.63 18 9710 893 9Dtral tobe craclu. 6 00 2.00 18 0330 934 1012 Superheating. May 21. 1884 3 25 0.00 18 7690 764 814 Charge large. 35 0.17 18 8250 790 845 4 00 0.58 18 8630 819 1 876 1 10 0.75 18 9030 847 910 : 20 0.92 18 9120 853 915 30 1.08 18 9240 862 926 ; 35 1.17 18 0310 H67 932 40 1.25 18 9360 870 936 5 00 1.58 18 9500 870 948 Central tube craeka. 03 1.63 18 9540 881 951 Superheating. May 26, 1884 2 25 0.00 22 8840 828 890 Charge large. 35 0.17 22 9081 845 908 45 0.33 22 9110 frl7 910 Ebullition. 3 05 0.67 22 0160 849 915 15 0.83 22 0200 852 918 35 i.n 22 0300 860 , 927 60 1.42 22 0330 863 930 1 • 4 20 1.92 22 W70 874 040 1 40 2.25 22 9450 870 040 Crucible explodes. June 9. 1884 2 15 0.00 19 716 ' (672) Charge large. 30 0.25 19 «••*•• •• 741 ; (696)' 1 45 0.50 Id 782 (735)1 3 05 0.83 19 855 (805) 1 15 1.00 19 o:t4 (880) 19 1.07 19 081 i (926) 20 t08 1.17 10 087 (930) ■rv 25 19 2864 987 930 30 1.26 (20) 40 1.42 (20) 28.*^) 975 920 55 1.67 (20) 2784 960 907 m ilO 1.92 19 2760 954 901 25 2.17 19 2707 054 9(n 40 2.42 19 2738 944 891 55 2.67 19 2737 944 891 5 08 2.88 19 2732 942 890 25 3.17 19 2755 950 890 40 3.42 10 2803 960 913 50 3.58 19 2809 968 915 Jnae 11, 1884 3 45 55 0.00 0.17 19 19 2808 970 915 .... ■•.••• 400 0.25 19 2800 969 915 07 0.37 19 12 V* V f 0.45 19 2848 982 925 18 0.55 19 25 0.67 19 2815 970 915 (72S •) 76 MEASUREMENT OF HIGH TEMPERATURES. Table 5. — CaMtancy of temperature in the later form of sine hoilinff-point apparaivm; time «frtf»— Continned. Date. Time. K. No. of thenno- couple. i 1 r.. T.iw Remarks. 1 A. tn. 1 June 11. 1884 85 45 0.63 1.00 19 19 i 2815 970 915 50 1.08 (23) 2806 970 915 58 1.22 10 2828 974 920 . 5 10 15 1.42 1.50 10 19 «••••• . 2824 972 916 25 80 1.67 1.75 19 19 2784 960 907 Jane 14, 1884 8 23 0.00 19 2811 970 914 3 47 0.40 19 2839 970 921 « June 21. 1884 4 35 0.00 23 999 939 41 0.10 23 ...... .... 2907 1002 942 55 0.33 23 2915 1002 943 50G 0.52 23 2919 1004 944 22 0.78 23 2935 1010 950 Jane 25, 1884 3 55 0.00 23 2809 ! 970 914 4 15 0.33 23 2809 970 914 4 40 0.75 23 2829 974 920 455 1.00 23 2829 974 920 • 5 06 1.18 23 2829 974 920 5 18 1.38 23 2780 960 907 In the experiments made on the 15th and 18th of April the charges were obviously too small. Hence we fail to discern a boiling point in the first instance and obtain irregular results in the second, in both of which cases the zinc vapor is superheated. In the next series the charge of zinc is much increased and the results are regular. The value of TsQ is slightly low, a result which may be attributed to various ex- traneous causes, such as slight corrosion or zincification of the thermo- couple, polarization errors in the measuring apparatus, etc. In this, as in the following series of experiments of the 30th of April, the temper- ature of the cold junction, in consequence of its unavoidable proximity to the furnac*^, rises as high as 70o. Otherwise both series are as com- plete as any we made. The effect of charging the furnace with fresh coal does not chill the retorts perceptibly, and the experiments were carried to an end without accident. In the series made on the 12tli of May, as well as in all subsequent series, the cold junction was kept at a low temperature (ca. 150) by submerging it in a current of running water. The values for Tjn found are lower than usual. The work done both on the 19th of May and ou the 21st of May was interrupted by breakage of the central tube. There resulted a diminution of the charge of zinc, in consequence of leakage, and the thermo-element soon indi- cated the presence of superheated zinc vapor. No boiling point is dis- cernible. The experiments on the 26th of May were a£:ain terminated at an early stage of progress by an explosion, due to stoppages in the efflux pipe for the zinc vapor. Both the elements No. 18 and No. 22 (730) BAKU*.] DEGREE OP CONSTANT TEMPERATURE. 77 were partially destroyed by these accidents, necessitating their replace- ment by No. 19. The constants and thermo-electrics of the new couple being different from the old, it is clear that the subsequent values for T„ are no longer immediately comparable with the preceding values for TsQ. To make them as nearly as possible comparable, however, the fol- lowing method was pursued : The values for e^o, corresponding to Nos. 19, 20, 23, and obtained on the 2d of February, on the 24th of April, and on the 12th, 26th, and 30th of May, were averaged, and this mean value was assumed to correspond with the mean values of T^^ given by TSo, 18 on the satne days, respectively. A glance at the tables below shows that on these days one of the series of elements, Nos. 19, 20, 23, and one of the series of elements, Nos. 17, 18, 22, were simultaneously compared. From these data the constants of the former set (Nos. 19, 20, 23) and a graphic representation were investigated ; from this finally we.took the values of T.a given in Table 5. In this way the break in the results is reduced to the least value i)ossible under the circumstances. • It is curious that in the subsequent work we were not able to obtain series of results as satisfactorily constant as in the earlier experiments* To speculate on the causes for discrepancy is of course futile, and the later data subserve no other purpose than that of comparing the thermo- electric behavior of the couples simultaneously calibrated. INFERENCES RELATIVE TO LOW PERCENTAGE ALLOYS. ..eduction of data. — In view of the insufficient degree of constancy observable in the above results as a whole, it is necessary to resort to an artifice by which all thermo-electric forces may be referred to a fixed interval of temperature, T— f. For the lower limit of this interval we selected 20^, a temperature as near the mean value of t as practicable; for the upper limit 930^, the assumed value of the boiling point of zinc. Then the reduction to the lower limit has the value e2o-e=(«-20) { a+b {t+20) }-, and the reduction to the higher limit the value 693o-e=(930-!r) {a+h {930+ T)). The method of correction was therefore a quadratic interpolation by which the thermo-electric interval is rectified at each end, and thus re- duced to the uniform temperature interval. The constants a and b were carefully redetermined in a final calibration, so that the sole re- maining difficulty in the equation is the choice of T. Fortunately it is only the variations of T with which the above equation is concerned, and this may be obtained either by linear reduction of the thermo- electric datum Tg to 930"^, or we may calculate the constants for each element throughout the interval Oo to 930°, and then use the T,n so obtained. The first method is less accurate than the second without being insufficiently accurate. At the same time the first method is so mach more expeditious that we applied it. (731) 78 MEASUREMENT OF HIGH TEMPERATURES. Table 6. — J'alues of c-o^f approximately , in microvolts. Date. : No. of I couple. e.1, ,030 January 29. 1881. January 29, 1884 . January 29, 1884 . Janoury 30, 1884 . January 30, 1884 . January 30, 1^ . February 2, 1884. February 2, 1884. February 2, 1884. February 2, 1884. February 2, 1884. April 24, 1884 Apill24.1884 April 24, 1884 Apja24,1884 April 24, 1881 April 24, 1884 April 24, 1884 , April 24, 1884 April 24, 1884 April 24, 1881..... April 24, 1884. ... May 12, 1884 May 12. 1884 May 12, 1884 May 12, 1884 May 12, 1884 May 12, 1884 May 12, 1884 May 12, 1884 May 12, 1884 May 12, 1884 May 12, 1884 May 12, 1884 May 19, 1884 May 19, 1884 May 26, 1884 May 26, 1884 May 28. 1884 May 26. 1884 May 26, 1884 May 26, 1884 May 26, 1884 May 26, 1884 May 26, 1884 May 26, 1884..... May 26, 1884 May 26, 1884 May 26, 1884 May 26, 1884 June 9, 1884 June 9, 1884 June 9. 1884 June 9, 1884 9,1884 Date. 1 . 18 9160 18 9150 18 9170 18 9180 18 9180 18 9180 18 9180 17 9320 18 91 GO 19 2816 18 9160 18 9100 22 9220 18 9100 23 2827 18 9120 24 770 18 9100 25 891 18 9090 20 2274 18 9070 18 0130 22 9280 18 9130 23 2830 23 2834 18 9130 24 7«C 18 0120 25 898 18 0140 20 2333 18 9130 18 9290 24 780 •>o 9080 19 2810 22 9080 20 2800 22 9060 22 9050 25 852 22 9000 26 2205 22 9040 24 817 no 9030 22 9122 MM 9080 19 2830 2u 2a-o H) 2830 1.'4 71M 10 •jRltO June 9 June 9 June 9, June 9 June 9 June 9 June 9 Juno 9 Juno 9 Juuo 9 June 9 June 9 Juno 9 Juno 9 Juno 9 Juuo 9 Juno 11 June 11 Juuo 11 June 11 June 11 June 11 Juno 11 Juuo 11 June 11 June 11 Juno 11 Juuu 11 June 11 June 11 June 11 June 14 Juno 14 Juno 14 June 14 Juuo 14 June 21 June 21 June 21 June 21 June 21 Juno 21 June 21 June 25 Juno 25 Juno 25 June 25 Juno 25 Juno 25 Juno 25 Juno 25 June 25 Juno 25 Jum^ 25 1884 1884. 1884. 1884. 1884. 1884 1884. 1884. 1884. 1884. 1884. 1884. 1884. 1884. 1884. 1884. 1884. 1884. 1884. 1884. 1884. 1884. 1884. 1884. 1884. 1884. 1884 1884. 1884. 1884. 1884. 1884. 1884. 1884. 1884. 1884. 1884. 1884. 1884. 1884. 1884. 1884. 1884. 1884. 1884. 1884. 1884. 1884. 1884. 1884. 1884. 1884. 1884. 1884. XHO.OI thermo- couple 9ji^^» 25 935 19 2825 26 2361 19 2828 30 7147 19 2824 81 3738 19 2823 34 5167 19 2827 83 4011 19 2829 32 1082 19 2830 32 1974 19 2830 19 2829 22 9383 19 2830 27 2908 19 2833 28 5030 19 2833 29 6482 19 2836 23 2830 19 2834 17 9250 19 2838 18 9330 19 2828 19 2832 34 5349 19 2833 33 6762 19 23 2835 34 5291 23 2834 33 8951 23 2835 32 2018 23 2839 28 2830 31 8751 23 2830 30 7095 23 28S2 29 0U6 23 8833 28 5029 23 2832 27 2974 23 2819 (732) BARUS.] DEGEEE OF CONSTANT TEMPEEATURE. 79 From this table it is expedient to select the mean values for each element, and then to arrange the alloys in a series of the kind described on page 80. This has been done in Table 7, where, in addition to ^a © ® ' ® > the constants a and b^ derived from the last definite calibration, are in- serted (microvolts). The interval of calibration for a and h is only (P to 401)0, as has been stated. Knowing, therefore, e, a, and b we are able to compute Ts, or the exterpolated value of the zinc boiling point, to which special reference will presently be made. The figures for e in parenthesis will l)e referred to in Chapter II. Table 7. — General summary of results. Series No. No. Descriptiou of element. 17 ; Pt (h); PMr, 20%; annealed 18 .do 19 Pt (h); PMr, 59o; annealed I^ 20 do I 22 j Pt (h); Pt-Ir, 209b; annealed. 23 ' Pt (b): Pt-Ir, 5%; annealed . 24 °{ in Pt (h); Pt-Ir, 296 ; annealed .. How, where, or by whom made. Paris metallnrgists.. .do. do. .do. do. Mean e. .do. IV ^ V^ 25 Pt (s); Pt Pd, 396 ; annealed.. 26 Pt (8); Pt Pd, 109^ ; annealed. . 27 Pt-Ir, 59o; I't-Ir, 1096; an- nealed. 28 PMr, 596; Pt-Ir, 1596; an- nealed. 29 Pt-Ir, 596; Pt-Ir, 2096; an- nealed. Pt-Ir 596 fused into Pt (a) in proper ratio, at Lab., OHs blast. rPd alloyed to Pt (8), ( at Lab., OHt blast. Pt Ir 596 and Pt Ir 20% wires fused together in proper ratio, at Lab., OH, blast c (9412) ( 9285 r (9345) < 9166 C (2861) ( 2823 r(2869) i 2S27 c(9453) i 9230 r 2829 ( (2883) 791 a. 7.60 -fO. 00390 -f 0.00385 -0. 00010 —0.00009 I 7.60 3.07 i 3.05 I 7.00 ! +0.00393 |(2.97) (+0.00047) 1.88 M). 00150 iS 98a ! 0.287 0.975 30 31 32 33 34 Pt (com.); Pt(com).Ni, 596; annealed. Pt (com.); Pt(com)-Ni, 296; annealed. Pt (com.); Pt(com.).Ir, 3%; annealed. Pt (com.); Pt(com.)-Ir, 5%; annealed. Pt eom.); Pt(com.)-Ir, 7%; annealed. ! Ni alloyed to Pt (com.), at Lab., 0H« blast Ir (com.) alloyed to ^ Pt (com.), at Lab., OHs blow-pipe. 2297 r 2941 *5030 6440 7121 3744 1998 3981 5336 2.36 3.89 +0. 00119 +0.00273 +0.00152 +0.00208 4.51 i +0.00398 8.43 4.56 L98 3.64 4.70 +0.00050 +0. 00005 +0. 00052 +0. 00147 +0. 00207 r- 861 887 960 973 856 970 (*) 797 760 828 834 835 825 833 844 833 842 * Imaginary. Series of alloys. — Having reached this stage of the inquiry, we are prepared, so far as the set of data at present in hand go, to bring the ooDSiderations back to the probable properties of the zero elements, (733) 80 MEASUREMENT OF HIGH TEMPEEATURES. platiDum-platinum, when these element are regarded as the limiting cases into which any series of therinoconples of platinum alloys must ultimately converge. A series of couples such as is hero understood has alreaily been defined. In each member of such a series pure plati- num is thermo-electrically combined with an alloy of platinum and a second metal, and the amount of the latter metallic ingredient decreases from alloy to alloy of the series as far as zero. Having given a number of thermocouples, -4., -B, C, D . . . , let the cold junction all be kept at the same Qonstant temperature, t. In like manner, let tiie hot junctions bo exposed together to a second tem- perature, which, however, is made to vary continuously from a com- pai'atively low value to as high a value as may be admissible. Then will a comparison of corresponding values of electromotive force indi- cate in how far the variation of the latter with temperature may be re- garded as uniformly continuous. Thermoelectric anomalies, such, for instance, as are presented by iron, nickel, probably by some platinum- iridium alloys, and by all metals at sufiiciently high temperatures, are thus detected and located. In practice it is o 4290 4370 4770 5700 6140 7910 7970 8370 T---- 1470 2510 8380 I. 8R00 ' 0470 I' 11010 I 12330 ' 1C940 |! 17210 18360 : 810 13:)0 22:)0 4280 5600 7018 7080 t %:}^'' Pt p«i ;i'^^^ii No. 13. I x\.'ik jNo. 14. 800' Pt, Ni. No. 12. 680 1150 1900 ]I 4200 ;. 5970 78rK) 88:'.0 810 1350 2706 3130 4(>40 6990 7750 i Pt. PtIr iPt. Ptlr 20%. , 5<^o. No. 14. I No. 10. 1830 2090 5120 5500 \k 7000 9450 10210 mp 2900 ! 8430 8470 8670 0030 9550 13190 1028 2G05 2610 2500 2660 2720 3000 1200° At the end of this table the approximate value of the temperature reached in eJMjh of these comparisons is given. The values of electro- motive forces in this table (No. 14 being the couple common to all) show that the variations are pracrically uniform, so far iis the compari- sons go. The table supplies an oxperi mental test, which corresponds (7;u) BARU8.] DEGREE OP CONSTANT TEMPERATURE. 81 very closely to the mathematical examination of a function for conti- nuity. If any equation between electromotive force and temperature, such a one, for instance, as e=a{T—'t)+b{7y — t^), were rigidly true for all ranges of temperature, T, then our methods would enable us to calculate the constants a and b from measurements of e, 7, t, made at tem- peratures not exceeding the boiling point of mercury, with a degree of •accuracy which would introduce a perceptible error Only at very much higher temperatures. If the thermo-electric equation hold, in other words, the calibration of a tiiermocouple throughout an interval of tem- perature within which a glass-bulb air thermometer is quite available, would enable us satisfactorily to measure temperatures lying in the regions of white heat. But such extrapolation is unwarranted because we possess no known criterion for the temperature above which the assumed equation appreciably fails. • In our original endeavor to surmount this difficulty we ventured to reason as follows : Suppose there be given a series of thermo couples of the kind specified, in all of which platinum is the electro- positive metal and the platinum alloy the negative metal. In such a series the con- stants a and b both vanish with the amount of foreign metal alloyed to platinum. Hence the relation between electro-motive force and temper- ature is ultimately linear, and, a fortiori, within the limits x)rescribed by the foregoing paragraph, the assumed equation will apply more accu- rately as the couple approaches the final couple platinum-platinum, from which the foreign metal has been wholly eliminated. If the quad* ratic equation (1) is more than an empirical relation, it would be practi- cally sufficient at an earlier stage of progress; i. e., it would be practi- cally sufficient for couples lying between platinum-platinum and a couple the electronegative part of which contains a certain determinate addition of the foreign metal of the series under consideration. To illustrate the manner of using such a principle, let a series of couples whose constants are known from a calibration between 0° and 350° be in hand; and then let a given fixed temperature (the boiling point of zinc for instance) be determined by each of them. There will be as many values for boiling point as elements. If we regard these as func- tions of the respective quantities of foreign metal in the negative parts of the couples, and if we represent the calculated boiling points as ordi- nates, and the percentage compositions of the alloys as abscissae, we obtain a locus the nature of which may be sufficiently obvious to enable us to prolong it as far as the axis Y. The point of intersection, there- fore, approaches very closely to the datum of the hypothetical element platinum-platinum. If the effect of alloying metals were merely that of joining them in multiple arc, the interest which belongs to the problem in hand would fit once vanish. Fop if ei and $2 be the electromotive forces of two wires theniio Qhx* BaU, 64—6 (735) 82 MEASUREMENT OF HIGH TEMPEUATUKES. [bull. W. trically combined with platinum, and if Wi and tOt be the resistances of these wires, then where e is the equivalent electro-motive force. Hence if r=zWi \ tTg, which may be abbreviated From this it follows that '=-W^^^1^-0- If in tills equation ?r2=x, which supposes this metal to vanish from the alloy, and if additionally aj and bi be made equal to zero, we arrive at an expression of T in terms of §. This result shows that however near we may approach the limit couple platinum-platinum, any thermal datum derived by thermo-electric means will none the less be depend- ent on the properties of the metal combined in multiple arc with pla- tinum. In the case, however, of metals alloyed, the results are quite diff'erent; for here the thermoelectrics of the alloy bear no intelligible or general relation to the ingredient metals of the alloy, so far as our present knowl- edge goes. Indeed it is not infrequent to tind the admixture of an electro-negative ingredient i)roduce a distinctly electro positive result. And hence it follows that constants referring to the final or infinitely dilute alloy have a special and unique significance. In the final alloy we have one metal combined by fusion with another in such a way as to produce absolutely no variation of molecular arrangement. If, therefore, data for the limit couple be investigated, they are those from which a clue respecting the dependence of the thrrmo electrics of the compound upon those of its constituents may most probably be obtained. Table 7 shows the sensitiveness of couples to be frequently' such that the final element platinum-platinum mtiy be api)roached very near, and it is for this purpose largely that the table was drawn up. With the object of basing the discussion on electric data exclusively, the constant a may be taken as a symbol of the composition of the alloy-component of the thermo-couples of a given series ; and hence the cnrves or loci here in question are obtained by representing any fixed datum (for instance the valueof the boilingpoint of zinc which obtains for the special couple under consideration) as a fuuction of a. We have attempted this with (730) BABU8.) DEGREE OF CONSTANT TEMPERATURE. 83 tbe data in hand, but tbey are not yet in sufficient number to give any definite hints as to the nature of the relations sought. It is necessary, moreover, to confine such work to data obtained from scrupulously pure platinum and from scrupulously' pure alloys — conditions which in CAse of the data of Table 7 are not vouched for. Indeed the table gives evi- dence of the varied character and purity of platinum derived from dif- ferent sources and shows a widely different electrical behavior of nom- inally the same alloys. There is one respect, however, in which the data of Table 7 are crucial. They show that extrapolations baseeriment.* The de- gree of error to which the observer is liable, the degree of constant tem- ];erature attained, the selection of substances having convenient boiling points, and finally the application of the apparatus to a variety of sub- stances for boiling-point measurement will constitute the chief topics of this chapter. The boiling-point apparatus must of course be such that ebullition may bo kept up indefinitely. APPARATUS FOE LOW BOILINO POINTS (100° TO 500O). Original forms of hoilingpoint tube. — The original forms of boiling- point ai>paratu8 for mercury, for Sulphur, and for aniline, water, etc., are given in Figs. 7, 8, 9, drawn to a scale of J. They are all constructed on essentially the same principle, slight modifications being introduced to meet each case. The apparatus, Fig. 7, consists of an ordinary gla^ lamp chimney, aaaa^ inverted as shown, and closed at its lower end by a plaster of Paris i)lug, hh^ surrounded by a wroughtiron cap, cc. The cap cc is larger than the glass, and bj' pouring in the plaster in the moist condition and allowing it to set, the tube is firmly secured between • Since th(^ (M)iiipletion of the work of the jircseut chapter, M. Le Chateller has made pjromotric V'xperimentH wjtU coUa iu view Bimilar ^o ^liofte here proposed, (Cf, p,{|0.) ift H4 (738) PIQS. T, 8. and S.- »' ^", 4 ?»:; ;*■■ "-i f* fe c ^. ' ft # -'.•-> ' ■.» ^i'* ■•» "t. ''■ ■•• • . I -i. •t. . -J. - - . r ^ * f'r. ' • .■•' '"* •■ t ■-i' »-». ^,- n. C. I BAKU6.1 CALIBRATION OF ELECTRICAL PYROMETERS. 85 the b(Kly of plaster within and a layer of plaster braced against the iron cap without. The cap cc carries an iron tube, dd, closed above but open b(4ow, and occupying a central or axial position with respect to the glass tube, into which it projects about two inches clear. The top of the hiiup-chiraney is closed by a suitable cork, ce, doubly perfo- rated, through the central hole of which is inserted a wide glass tube, /it, partially closed above by a loosely fitting stopper. Through the other perforation passes a glass tube, /.(/, by aid of which some gas (N2, CO2) may be introduced. The glass aaaa is partially filled with the substance whose boiling point is to be used (in the present instance mercury), only enough being poured in to submerge the central tube dd with the exception of about 0.5"" of its head. To keep the metal in ebullition, use is made of Dr. Wolcott Gibbs's ring-burner,^ rr, the flame of which is properly regulated. Very thin copper or brass gauze, or copper-foil, m wi, surrounding the part of the gla^ss tube encircled by the ring-burner, is sufficient to almost completely obviate the dangers of breakage; and a circular screen of thick asbestos, w w, bent in the shape of an inverted cone protects the top of the tube dd from direct radia- tion. Above wn it is well to surround the tube aaaa with a thick jacket of asbestos, p2>2^j>, extending as far down as may be without shutting the surface of boiling mercury entirely out from view. The mercury which condenses on the sides of the tube falls back in small drops into the mass Ik below. The process is therefore continuous. The properly insulated thermo-couple is intrdduced into d d from be- low, and the hot junction is pushed forward quite as far as the top»of the tube d d and slightly above the surrounding surface of mercury. A screen may be fastened a little below the cap cc to shut off all radiation from the cold junction, which is submerged in oil. The apparatus for sulphur in Fig. 8 differs from that in Pig. 7 only in that the wide central tube h h i i haa within it a second glass tube, qtj partially closed above with a cork. This second tube whenever the passage below is stopped up by the distillation of sulphur may be at once removed and a similar clear tubeinserted. A slow current of dry car- bonic acid gas entering at g ])asses through the apparatus during ebul- lition. Subsequent experiments showed that with suitable changes in the apparatus the tube h h i i as well as gas current could be dispensed with. This will be referred to again below. The sulphur condenses on the sides of the tubes and by far the greater part runs back into the mass k k below. There is a line of demarkatioh encircling the tube where the temperature is the melting point of sulphur. For liquids with a boiling i)oint below that of mercury and sufficiently low not to char a cork, the boiling tube may be considerably simplified in the way shown in Fig. 9. Here both ends of the lamp-chimney are closed wi^h a cork centrally perlbrated to admit a long glass tube, dd, *The Gibl)8 riDg-biirncrH were iiilroduccil into tbia laboratory by Dra. Goocb and Cbatanl, and bavo siuce become invaluable. (739) 86 MEASUEEMENT OP HIGH TEMPERATURES. [bull. 64. extendiDg quite through the tube aaaa and open -at both ends. The tube ddm wide enough to admit a mercury thermometer at its upper end, held in place by a cork, nrpos6 of vary- ing the pressure by any amount compatible with the strength of the tubes. It is also through h that the substance to be boiled is intro- duced. ' It is by means of tbis arrangement, that I purpose to study the relation between boiling point and pressure over long ranges, and for mercury, sulphur, and divers other substances. The thermo-ele- ment for such puri)ose must be calibrated with the reentrant glass air- tbermometer described in Chapter IV. Tubes of this kind I obtained from M. Emil Greiner, of Nassau street. New York. Glass of a ^ecially hard quality is made by Api)ert frferes, Glichy, France. Inasmuch as M. Troost was able to boil selenium in this material with impunity, the upper thermal limit of the glass boil- ing tube may be considered given by the boiling point of selenium. Tubes of the kind here de8cril)ed for investigating the boiling-|>oint pressure functionality are the simplest and at the same time the most m T ■ > ■ ^ ^ ^ rr. Gibbs^s ring-burner. — A final reference is to be made to the ring- bjirner. This is shown diagrammatically about one-half full size in Fig. 1 2. The burner proper, a 2» o, is a circularly bent tube of brass or iron, on the inner side of which about forty radially disposed holes, each about Q.V^ in diameter, have been drilled. The straight tube o/connects the ring with the injector, the tube d e admitting of the influx of gas, the tubo/o of the injection of air. Both the tubes d e and/o are provided with stopcocks. Where only moderate intensity of flame is desirable gas may be passed in at /and the tube deleft open. Either of the tubes deov of is available for clamping the burner in the ring stand. In the general case where a blast is necessary Professor Richards^ pneumatic injector is most easilj' applicable. The pump which can be used equally well either for slight compressions or for exhaustions is now in such general laboratory use that special description is unneces- sary. It is probable that for special purposes boiling tubes of larger diam- eter will be preferable, but such tubes are more fragile and the manip- ulation is of necessity less expeditious. APPARATUS FOE HIGH BOILING POINTS. Original forms of boiling crucible, — The tubes ju.^t described are no longer convenient when the boiling point of the substance exceeds low redness. In such a case bellows have to bo used for injecting air and the glass tube itself, becoming more and more viscous, yields gradually to the charge of metal it contains. Hence for high temperat'ires it is necessary to replace the glass tube by crucibles of fire-clay or of porce- lain. In Fig. 13 I have given the original form of an apparatus of this kind. It consists essentially of two French crucibles, aa a a and hbbbj put together on the flat open end, which it is well to grind smooth. Both crucibles are perforated. A porcelain tube, d d, has l>een ce- mented into the lower crucible with asbestos cement. This tube, closed'above, open below, and glazed exteriorly, is to contain the thermo- element. Through the tube g h above, some reducing gas, notably hydrogen, may be introduced, the tube g h being either glass or porce- hiin. The lower crucible is partially filled by the metal or other sub-- stance, A: A', whose boiling point is to be used, care being taken to in- (744) •■1 CALIBRATION OP ELECTllICAL PYROMETEEfl. 91 trodnce iio more than is just necessary to cover tlie central tube d^. Tbe lower crucible is surrounded bj' a furnace, FFFF, made of tbe same uou-couducting mixture wbich is used in Fletcher's small iujector furnace. Heat is coDimunicatcd by means of tlie iujectof blow-pipe A B C, gas entering at the tube C, air at D. Botii C aud E are provided witli stop-cocks. Xbe products of combustion escape at D. Tbe cru- Piu. 13. OriglDiilroi Scald. |. cible aaaa hn.s been litted iuto the bottom of FF, through which the central tube dd projects. All crnckw and crevices are closed up with carded asbestos. Ju this way the space below the furnace remains practically cold and tbe thermoelement may bo inserted or withdniwn with great convenience. A few screens protect the cold junction from radiation altogether. Perfected forHiM of hoiling point crucible. — Tliis double crucible appara- tus behaves e\cellenti.v uiilil tbe extreme white heats are reacbeil, after which the jiorcelain and the cement become viscous, aharu hin-e been uuiubered Hiuiiliuly to Fig. 13. A conical shape is here given We. Scale, |. to the cnicible, with the object of decreasing the essential charge of ziue and of thereby expediting the boiling. The fnrnace-body J'J'and lid ^ -F" are both jiroperly bonnd with iron, as shown at mm, Nim,min, and the body rests on a bed plate, of iron, s ^, provided with a hole tbrongh which the botttom of the crucible a a partly pmjects. Z Z is raised on rather tall legs, allowing the operator to munipnlate the thermoelements from below. The erncible projects above the fnniace, and the lid bbin shoLiIdt-n d. A batteiy of thiee or four of these fur- (74(1) BARU8.) CALIBRATION OP ELECTRICAL PYROMETERS. . 93 iiaces may be placed on the same bed-plate, in a row. Each furnace is provided with its own burner, all of which are fed from the same bellows and the same gas-supply (see frontispiece under Z>). It is best for this purpose to attach the bellows (Fletcher's pattern) to an engine, on a very short crank. The pressure of air may then be regulated by in- creasing the length of the crank. Burners constructed on the plan described at length below (page 183), only on a smaller scale, are prefer- able. They do not explode back. For very high temperatures two and even three such burners may be made to impinge on the same crucible. For cadmium or zinc a single burner is more than sufficient. At high temperatures the ettiux hole I> may be partially closed with asbestos. The products of combustion escape uniformly on all sides around the plane where the furnace-body and furnace-lid meet. A ring of asbestos, placed around the crucible to protect it from the fldme of the burner, is soon fluxed down upon it, and is apt tc destroy the cru- cible. A ring of baked fire-clay, however, is good. The crucible shown in Fig. 14a is intended for work in which the variations of boiling point and pressure are to be investigated. It is made of refractory porcelain and glazed within. The lid cab fits pretty snugly into the crucible e/d, so that the two may be sealed hermetically at the joint c d by sodium tungstate (Gooch) or other material. The tube at a is in connection with the air-pump. Such cr.icibles are avail- able for the ebullition of salts of selenium, cadmium, zinc, and probably antimony and bismuth in vacuum. Being made of porcelain they can be more elegantly shaped than fireclay crucibles, but they become se- riously viscous at a lowey temperature. A second form of boiling crucible is shown in Fig. 15. It differs from Fig. 14 only in this respect, that the central tube d d, which in Fig. 14 is closed just below the surface of the boiling metal, in Fig. 13 extends quite through the crucible imd out of the top. The latter form has the advantage that the degree of constancy of temperature along the length of the tube may be explored by inserting an insulated thermo-element. The part of this tube above the surface of ebullition is closed during the measurement with a fire cluy plug, and at the to[) with asbestos wick- ing. The form shown in Fig. 15 may also be used for annealing wires at definite high temperatures, by drawing th^m through the zone of ebullition by clock-work (cf. Fig. 10a). This form has therefore many decided advantages over that in Fig. 14, with the one serious disaxlvan- tage of being much more fragile. Fortunately it appears from the data below, that the more practical form. Fig. 14, is quite reliable as regards accurate value of the boiling points attained. In all cases the substance to be boiled, k k, must surround the tubes d d below the plane of the burners, even more than has been shown in Fig. 14. When this is the case no i)art of the tube d d will be at a tem- perature higher than the boiling point of A* k, a desideratum. In c»8^ of 2!n, Cd, »ud other uutals the crucible umst ])^ giuaed iu^ (747) 94 1CBA8DBEMENT OF HIQH TBMPERATUHES. tenially eitber witli borax, or with silicitte of soda or with some fusi- ble porcelain glaziiij;, otberwitte the vai>ore at once iiermeate tlic central tube d d and corrmie tlie tliermo-element within. The jirescuce of vapor may be discovered by inserting a poioehiiu pipe-stem into dd and rapidly withdrawinfr it. Metallic vapor, if present, aisuatly coats the white stick with a black metallic vcvcritig, which rapidly oxidizes. Jti, Sb, Sn, Pb, etc., Kliize the interior of the erucihlo in virtue of the fluxing j)ower of their oxiile». This con-osive action eventually becomes sufficiently active to eat its w»y through the central tube and discharge the contents through the lM)ttoni. A single crucible seldom will stand more than one ebidlition, bnt a Ringle ebullition may be prolonged many hours. If a zinc crucible be broken open whuu uuld the walls are found to be covered with a coat- (748) BABUfll , CALIBRATION OF ELECTEICAL PYROMETERS. 95 iug of metal consistiug of solidified drops of zidc, wliicli were distilled, recoudeused, and rau back again down the sides. In the saipe way the central tube is kept covered with a coating of zinc. Zinc dust escapes at the joint between lid and crucible, and eventually melts, forming an impervious joint. Zinc dust also escapes where 'the hydrogen tube enters the lid. In case of zinc and cadmium, this is an excellent dri- terion o£ ebullition. In all cases the burners aild to be shut off until the escape of metallic dust at h is only just apparent Metals like Sb, 6i, have no such boiling-point criteria, and whether or not the metal has boiled becomes a matter of conjecture. Tin charges slag so heavily that the metal is soon jacketed with a thick viscous coat and tiie state of the metal under it can not be known.* INSULATORS. A very essential part of the thermo-element is the insulator. The device which after very many trials I finally adopted therefore de- serves careful description here. These insulators are thin stems (0.45*''° in diameter, or larger), containing two parallel canals, as far apart (0.20*'™) as possible, and about 0.1*^™ in diameter each. In order that these stems may be of value, they must be made in a way which affords a perfect guaranty that throughout the length of the insulator the canals nowhere coalesce. The following machine, Figs. 16, 17, by aid of which insulators of almost any diameter and with any number of holes or canals may be made in lengths of 25*'"* to 30*'*'* or more, gives full warrant to this assumption. The tubes are simply x)ressed after the well-known manner used in the manufacture of lead pipe. In Fig. IC (scale J) A 5 is a thick scantling, pf wood, fastened ver- tically, to which a short cross-scantling, (7, is firmly braced by bolt- ing two boards, shaped as in the figure laterally against both A B and B C. B carries a barrel of strong gas-pipe, a a a a^ out of which the porcelain is to be pressed. To secure a aa a the piece has been cut apart in the middle parallel to the plane of the pai)er, and the hole for the barrel is somewhat scant. Hence when the two halves of are drawn together by a couple of strong bolts the barrel is almost im- movably fixed. The barrel is surmounted by a cap, cc, through which passes a piston or plunger, d e, which can be moved up and down by the handle//7 in the way which the figure readily shows. The lower end of the barrel is closed by the die-cap h h. A lateral hole, ft, allows of the introduction of porcelain or tire-clay slip until the barrel is quite filled. Downward motion of the plunger forces the slip through the ^ ExporiiiKMits «iuco made with the cruciblcH, Fig. 14rt, showed that the vacnnm boiling point of Bi is easily reached. To get a tight joint at e rf, the space between lie varied at pleasure. It is also obvious that the number of canals is immaterial so far as the a[iplicatiOD of method is concerueiH» lyt'ro fusicued tq l\\v ylinj^et, (150) t • - ' ! \ P \ ,* I J' I'.' •R BAKL'S.] CALIBRATION OF ELECTRICAL PYROMETERS. 97 the crucibles (Figs. 13, 14, 15), but they become electrically conducting and are objectionable. Insulators of lire clay are therefore preferable, Inasmuch as they are at least as refractory as the crucibles, and Messrs. Hall & Sons, of Buffalo, to whom I sent the above machine, succeeded excellently in making them. Work with fireclay calls for great expe- rience and skilled manipulation, and it is therefore best to put this work into traineasses through the large rheostats E Ri and then to n, completing the third branch. When the current is zero in O e=E j,rz where e is the electro-motive force at e, Eihe electro-motive force at E in the figure; where B is the resistance at R R\ and r the resistance at r in the figure. By means of the key K two circuits conveying currents due to J? and e are closed simultaneously. It is, however, essential that they besoclosed as to act differentially on the galvanometer G at once. Other- wise there is danger of throwing the needle violently against the stops. Hence in filling the cups of mercury K^ Kit K^ care is taken to keep the level of mercury in E% and ^3 decidedly above that in /ii. When the metallic prongs of the key descend to close the circuity, the one not passing through the galvanometer is closed first, and a moment after the differential current passes through G at once. A diagrammatic section through the mercury cups of iTis given in Fig. 19. The make- circuit strip K' is of amalgamated copper on a si>ring which keeps it open against a stop. Circuits may, therefore, be made and broken, almost instantaneously. The object of the key C is to enable the ob- server to use pairs of the resistances of the biidge rheostat r, either in series or in multiple arc. By connecting C4 and Ci only, these resi}^t• ances are used in series; by connecting rj Miid c-i as well as C3 and C4 they are used in multiple arc. The available resistunces are thus 0.05, 0.10, 0.20, 0.5, 1.0, 2.0, etc., as far as about 20,000. The fine adjustment is made at i^, which is variable in single units whose mean value is al- ways large. Varying r in steps, in this way, greatly facilitates the comi)Utatiou, The electro motive force obtained as above is never wholly due to the thermo-element at 1\ P2 alone. It contains a disturbing electro- motive force £, resulting from the accidental distribution of temperature, iu connections which can not be thermo-electrically identical throughout. For a short period of time (that of an observation) e may be considered nearly constant, or at least varying linearly. It may therefore be eliminated, very nearly at least, by two commutators, A and B^ a« Dr, (752) BABU8.] CALIBRATION OF ELECTRICAL PYROMETERS. 99 Stroahal and 1 have shown.^ In a series of corresponding positions of these commutators, alternately opposite, the direct measarements would give + e+£ '^e + sil + a) +e+€(l + 2a) ^^- = «i5— -— ^-^— • = «2; ^ -^+>; - - = a3;etc. where an odd number of observations is made. Let Mi be the mean of the odd right-hand members, and 3/a the mean of the even right-hand members. Then ^=l(Mi + M,). In the case of small electro-motive forces this elimination is essential. Standards of electromotive force, — Inasmuch as all measurements are based upon the constancy of the double Daniell ^, it is obvious that the value of this electro-motive force will have to be frequently tested. This can be done very simply and with accuracy by replacing the thermo-couple by a Latimer-Clarke or other standard element and pro- ceeding with the measurements as usual. It is to effect this compen- sation that the rheostat r must have a large resistance, 20,000 ohms, available. For thermo-electric work r = 0.1 to 500 ohms suffices. For a similar reason two Daniells are used instead of one. Currents are made only momentarily, and approximate values of r and B are always known. The constancy of my Latimer-Clark's cells has certainly been exemplary, and it was thus easily possible to reduce the Washington results to the older results obtained in New Ilaven in a way that estab- lished the general accordance of data beyond a doubt. In addition to the Latimer-Clark standards, I possessed for comparison a number of siphon Daniells, certain Beetz's dry Daniells, and a special form of nor- mal Daniell of my own which merits description. In this battery it is impossible, correct usa^e presupposed, for the copper sulphate to con- taminate the zinc. Zinc and ziuc sulphate, copper and copper sulphate, are kept in separate bottles, and are only in electric contact during the few minutes of measurement. In Fig. 20 the ZnZn SO4 bottle is on the left, the Cu-Cu SO4 bottle on the right. Each bottle is provided with an h-shaped siphon of glass, the longer shank of which, a 6 c, is closed above by a rubber cap, a, and below by a cap of parchment paper tied on. The shorter shank d dips into a little vessel, A^ containing Zn SO4 in solution. When not in use the siphon tube is nearly empty. Before using both tubes are rinsed thoroughly with Zn SO4 solution by com- pressing and relieving the caps a. When clean they are filled in the same way with the Zn SO4 of the dish A, After using, both siphons are emptied by working the cap a as usual, and the ends d are closed by si)ecial caps (not shown) to prevent evaporation. It is obvious that if the rinsing be properly done Cu SO4 can not possibly get into the zinc flask to contiiminate the metal. Zn therefore remains bright for years. * Bull. U. S. Geol. Survey, No. 14, p. 3o, (753) 100 MEASUREMENT OH* HIGH TEMPEKATUBES. [dull. M. Results obtained by comparing divers utaudard eleiiieuts A^m 1SS3 to 1SS8 are given in tlie next tables. Unfortunately time-magnutio measuiemeuts are not feasible in our laboratory, vitli a degree of cer- DsDlolL Scalv, I- twnty to wamint their adoption. Nevertlieless by comparing Latimer- Clark and Danieil standards, the respective tendencies to variation of AvUicli are probably of an op[>osite character, souiit corroborjilive in- formation may be obtained. In tlienc^it tiilile the time or date of com- parison is given in tbe first column. The next tjve coluinna contain data for Latimer-Clark elements, of which ITos. 7), H, F were made by myself. ^os.lllaud 115 are Elliott standardn. Curiously enough, the latter are neither as rigorously constant, nor is their internal resistance a» small relatively as is the case in my own standanls. I have reason to believe that one or both of the Elliott standards suffered by trans- portiition, for in the examination made in 18S7 No. 115 was fount) entii'ely out of oixltrt and was necessarily discarded. In the siphon Daniells the two jars are like those in Fig, 20, except in so far as they arc iierinaneutly joined by a siphon. This siphon is filled with zinc Bulphato through a small vertical tubnlure during use, and emptied after using. With all precautious, however, It is impossible to keep the copjier sulphate from difliisini;; into tlie zinc jar and corroding the metal. Hence this siphon form is inferior in eflicieucy to the se|>arate cell form (J already described. IJeels standards' are also made by myself. Electromotive forces are given in volts. (754) I. aa, 1864, p. loa. CALIBBATION OP ELECTRICAL PYROMETERS. Table 9. — Comparison of itandard «lemenfi. Lb timer- Clirk nlBndirda. SlaidBid DsQli'U cell*. DiUf. SlpboD Joioed ulli «l]* """ar- Tern- per«- "^ E. F. Elliott, KUlDtt, 0. ff. '. 9- n- .. *■ 18SS i.*sa I. JIB 1.42D {1.0B6) l-OJll (•) - lB8i i.oso i.asi Oa,38, I8B5.. Uu. 21 1MB Aug. tJ, 1887 1.884 1.350 I.3WI 1.075 l.OKl l.Wil 1.U81 ;i9= ImiiiHllatrlT after b(Wde the Liitlmer.Cli '- -ledintelv i>n«r n1»1iifl|t1lif])Bplell O. J inllntelT aFiar rettlvioft tH Elhittt *u lediuwiy after Akkiifg 0e IiiliMl ^ iS: Odrdj. In the construction of this table the element '/> i% nskiiBif^l'-th- h^Xoi^': Rtniit, and with tliis premise tlie data of the table are at once inttll^-*. ble. I need only remark that my Latimer-Clark staudards, an compared with the separate- eel led Baniell Q during the seventeen months of ob> servation, are as good as absolutely constant. It is for this reason that I am warranted in placing much confidence in the data of both these conplcB, of which the Daniell has the advantage of constancy and the disadvantage of less facile manipulation. The siphon Daniells are in- ferior to the form Q, as are also the Beetz patterns, concerning; which, however, it is necessary to remark that the gypsum mixture of copper sulphate and zinc sulphate solutions were probably too moist. I found after a time that the line of demarkation had disappeared and that the solutions must have dill'used into each other. It will be seen that the elements J), £, F, though identical among themselves, difier conaidenibly from Elliott's Latimer- Clark's ; not more 80, however, tbau Elliott's elements differ among themselves. A much more carious result was obtained in measuring the temperature coelff- cients of the siphon Daniell's and the Latimer Clarke's. To do tliis the elements were first covered witli melting snow and afterwards sub- merged ill water heated to different temi)eratures. Measureiueiits were matle by the zero method described, and to give additional certainty an -auxiliary Daniell was used for comparison. In other wonis, the ele- ments g, h, i, JFJ, F, heated to the temperature spocilied, were compared with J) and li kept cohl, by inserting them alternately in the satne cou' nections ; P was compared by a galvanometer method. The main com' parisons were made in 1S83, certain corroborative data added in 18S7, a is a mean constant, derived graphically :i 1.075 N t 0. I. E. a Menn temperature co- efficient of a, II, I. 1.0C9 14 1.073 Between (P and 30°. 15 1.073 15 1.073 a=-f0.00021. 24 1.074 33 1.076 43 1.075 51 1. 075 . The electromotive force and teruperature coefficient of the Latimer- Chirk standard has been much discussed. Besides Clark's^ original in- vestigation, V. Ettinghausen,* who cites the relevant researches (Clark, Helmholtz, Kittler,Ui)peiil)orn, Alder Wright) and Rayleigh' havegiven it critical study. My own temperature coefficient is smaller than that ordinarily given, and indeed so small as usually to be negligible. The ' Clark : Jour. Soc*. Td. Eiiginoors, vol. 7, 1H78, p. 53. *v. EttiiighausiMi : Wienor Zeitschr. f. Eloctrotecli., lHrt4, p. 1. 'Rayleigh: Rcpt. 54th Meeting Brit. Assoc, Adv. Sci., 1H84, p. G51 ; Proc. Royal Soc., London, vol. 40, lcJ86, p. 79. (75G) iUfct».l CALiBftAtlOlf 01^ ELECtRlCAL MrOMETEES. 103 cause of this variation may be songht for in the composition of the mixt- ures. I have, moreover, kept the paste wet with a layer of zinc sul- phate, in this way decreasing the internal resistance. In the case of zero work, standards with enormous internal resistances are undesirable, because all necessary resistance is introduced by the rheostats. I made a number of experiments to study the dangers due to polarization in the batteries, and it is the outcome of this work that the large resistances in the connections have been retained. The data themselves are su- perfluous here. METHOD OF COMPUTATION. Many experiments go to show that the quadratic relation where e is the electromotive forkeSojc the-temj^eraturjes T and t of the junctions of the thermo-elemeut alitla And i^w^ cSoflstapts^i^ a xery com- plete interpolative equation, so long as the temp6ratiM3e TiSriot t^o far' above red heat. In general, however, it is desirable to express e graphio- ally for each element. The method of measuring e has just been indi- cated. T is the temperature given either by some known high boiling point or by direct evaluation with the air-thermometer, while t is di- rectly read off by a mercury thermometer. If the graphic chart thus obtainable is subsequently to be used for tem[)erature measurement, it is desirable to refer all values of e to C20, i. e., to the electromotive force which obtains when the hot junction is at T^, the cold Junction at 20^. This correction follows easily from equation (1), for if e =a(T-t) +b(T^^t^), and 620— e=a (f— 20) +b (f^-iOO). The constant a and b may be determined from the steam and mercury vapor calibration. A table is then to be constructed for the correction ^80— c as varying with t By adding this to any given value of e the temperature results are at once comparable with the values of the chart^ in which e is represented as a lunction of T. t should of course be kept as near 20^ as possible. In the measurement of e, a small table in which the log r is once for all inserted for each r, and another in which the log E is inserted for each Ej greatly expedite the computations. My original plan of calculating the constants of « as a function of T and t by the method of least squares was soon abandoned. These con- stants do not represent the function truly, and since many calibrations are to be made the computation becomi s excessively laborious. Finally, T can be taken from the interpolation chart quite as accurately as it (757) 104 MEASUREMENT OF HIGH TEMPERATURES. [bull. M- can be measured and with mnch less liability to error. If equation (1) be solved with reference to T it follows that — T=(V^-.)| where When many values of T are thus to be found the computation is by no means unlaborious. By keeping r constant, and varying By a table can be calculated once for all, for the function in which a mean value is inserted for K Ruch a table for frequently recurring values of the arbitrary opfistftnf f aii4 for values of By increas- ing in arithmeti^l puog^^sion.T^^i. a'«diffeTence of 1,000, is of great , > piervice in la^i]itaSting.llire cafculation of e. It insures greater exemp- '•' tiou fiiom^etron A small correction for U is only necessary to correct the interpolated results. Instead of applying a zero method like the present, it is of course permissible to use simplified processes in which currents only are meas- ured. A torsion galvanometer, such, for instance, as that actually used by Schinz (1. c, p. 49), suggests itself. By the aid of my boiling tubes and crucibles the scale of such an instrument may be at once graduated in terms of the centigrade thermometer. Not only can this be done with a great degree of accuracy, but the thermal calibration of the galvanometer may be checked with ease as often as desired. There can be no doubt that for practical purposes this apparatus is exceed- ingly convenient. Nevertheless the measurement of electromotive forces by the zero methods here discussed retains an advantage over current measurement, because measurements of electromotive force made at one time may be at once compared with corresi>onding meas- urement made at any subsequent time. The data are easily expressed in terms of a fixed absolute standai*d, in other words. All this is much more difficult in the case of current measurement, even if it were as accurate, for current measurement brings in the arbitrary constants of the galvanometer. EXPERIMENTAL RESULTS. Exploration for constancy of temperature ^ watery aniline. — When the boiling tubes. Figs. 7 to 11, are to be used for temperature measure- ment, the chief ]>oint of interest is the degree of constancy attained throughout the length of the central tube into which the thermo-ele- ment is to be inserted. To obtain the requisite delta it is sutllcient to in- sert a thermoelement, the constants of which are approximately known, into the tube mentioned, with the junction consecutively at different (758) BABU8.] CALIBRATION OP ELECTRICAL PYROMETERS. 105 heights above the surface of ebnllition. In the following tables, there- fore, the absolute valaes of the high temperatare T is of less importance and of smaller accaracy, while the variations of T are represented with nicety. In the table the temperatnre t of the cold janction is constant; e (microvolts) is the measured electromotive force of a new element, Pt hard-Pt Ir 20 per cent., from which the temperature T is computed. Table 12. — Constancy of temperature along the axis of boiling tube. Steam. T=100^. Heieht of janc- tion above bottom. 1 r. Remarks. Chn. 1 Micro- o(7. I volts. oC. 6 20.0 660.7 08.9 Sarronnded by liquid. 10 20.0 673.0 100. 1 Surrounded by vapor. 16 20.0 672.2 100.0 Do. 20 20.0 672.0 100.0 Do. 25 20.0 672.0 100.0 Do. 30 20.0 672.0 100.0 Do. 34 20.0 666.0 99.4 Sarronnded by cork. 5 20.0 683.7 101. 2 Surronnded by liqaid ; bamer lo'vrered. This table is cited as aa example of many similar observations made with like results. The adjustment of heat was nearly perfect, so that no steam escaped. The ebullition was quiet and the water was left in the tube in almost undimiuished amount at the close of the experiment. The first observation 5^™ above bottom of tube is taken at about the middle of the boiling liquid and the temperature here depends upon whether the ring burner encircles the tube above or below this point. The next observation, 10*"™ from the bottom, is about 2*'"* above the surface of ebullition, and from here to the upper cork the temperature is absolutely constant. To make these explorations it is necessary that the thermo-couple be new or perfectly homogeneous and annealed; other- wise the error of homogeneity will be falsely attributed to an error of the constancy of the boiling tube. Exploration with a mercury ther- mometer is less satisfactory than the thermo-couple test because the Bten\ of the thermometer usually projects. Similarly constant results may be obtained with aniline at 187^, which it is therefore not necessary to cite. They show that with the junction about 1^™ above the zone of ebullition, quiet boiling presup- posed, its temi)erature may be regarded identical with that of a mer- cury thermometer placed contiguously with the mentioned junction and inserted from above. Exploration for constancy of temperature ; mercury, — In the case of mer- cury the zone of constant temperature is of course much less in height, and special investigations with respect to it are therefore essential. The data in the table are given on a plan identical with the foregoing. Results are also appended for mercury impure with oxide, in which (759) loe M£ASURfiMCNt 6P ItIdH TEMPSRATtmES. (bull.^ case the liquid sometimes bnmps violently dariug ebnllitioD. The liquid surface is at 10^"* from the bottom nearly. Table 13. — Conatanoy of temperature along axis of boiling ,tube. Mercury, T=358^. Height of junction above bottom. 9. t 1 T. 1 KemarkB. Cm. JltVro- volUt. 1 In Uquld I J J 21.5 21.6 3320 3414 347.4 358.0 1 #11 In vapors ^^ 21.5 3131 357.0 1 Fresh morcary; brisk and regular 21.5 21.5 3121 3410 356.2 355.2 boiling. Liquid surface at lO'*. 1 15 21.5 3330 348.2 In liquid >! 8 I 9 21.5 3303 353.9 2i.r» 3448 358.4 Fresh mercury ; brisk and regular 21.5 3436 337.4 * l>oiling. Liquid surface at lO^-*. In vftpor { , ^ c 15 21.5 21.5 3436 3102 3:)7.4 356.4 Disks in the mercury tube. 1 5 24.0 3425 858.2 > Violent boiling with bnmplng. 15 24.0 3393 325. 3 I 5 Liquid Murface at 10«-. 20.3 3856 391.3 • 5 21.7 3300 345.8 23.0 3436 358.8 10 1*2 15 22. 9 23.4 23.4 3431 3295 3090 357.8 346.0 329.1 Gentle ebullition with bumping. Liquid surface at 10». 20 21.8 745 94.5 25 21.8 443 68.2 30 21.8 317 42. 6 ' J These tables show conclusively that for a distiiiico aloiiYROMETERS. 107 stant temperature may be macb iDcreased. It has been stated that in the data of Table 13 the variations of boiling point, and not the abso- lute value of the boiling point, is the point of consideration. Hxploration for constancy of tempertUure; sulphur. — From the nature of the case, the calibration with sulphur is more difficult, and calls for a more careful examination. Hence series of data are drawn up in Table 14, both for gentle and for violent ebullition. The condition of con- stancy of the center of the zone of constant temperature is also tested by a special thermo-couple, inserted from time to time during the prog- ress of the measurements. In the first part of Table 14 the surface of ebullition is at 12^°* above the bottom; in the remaining parts about 8.5^" from the bottom. No carbonic-acid or other gas is introduce^ into the tube, and ebullition probaby takes place in SO2 gas, formed from S vapor and the oxygen of the tube. To produce very violent ebullition the copper gauze surrounding the sulphur tube was heated even to red- ness. As before, the variation of T, and not the absolute value of the boiling point, is the chief consideration. Table 14. — Constancy of temperature along eucis of boiling tube. Sulphur. T=4490. Height above bottom of tube. t. oa 15 15 15 16 16 16 16 16.6 17.2 10.0 19.0 19.0 19.0 19.0 19.0 19.0 19.0 19.0 19.0 19.0 19.0 19.0 19.0 19.0 19.0 19.0 19.0 19.0 e. Micro- voltt. 3056 4038 4203 4220 4273 4167 3394 4206 4198 3923 4498 4517 . 4545 4029 4651 4577 4078 3448 2779 3886 4487 4.''>00 4515 4587 4643 ; 4509 ' 3988 ' 3221 T. o(7. 339 433 4i8 451 456 445 373 449.5 449.2 398.9 445.0 446.5 448.5 455.3 456.8 451.4 411.9 359.3 301.0 395.9 444.0 445.4 448.0 452. 1 456.5 445.8 403.8 839.6 Time. Remarka. Crn. MS 1 1 Burner at lO*". Liquid surfaco at 12«-. < l^Iild ebullition. Liquid sur- faco at 8.5*". 1 Mild cbuIliUon. Liquid ut 8.5«-. In vapor. < In liquid.^ u 13 ■11 10 9 8 12 12 13 11 h. tn. If 30 12 Id 2 16 p.m. In vapor. < '" 10 In liquid. < f 8 7 6 5 4 .1 fl3 J" In vapor. < , 10 I r 8 7 Inliqui.l.^ 6 5 4 i 3 15 ' 1 (761) 108 MEASUREMENT OF HIGH TEMPERATUREfi. [boll. SL Table 14. — Constancy of temperature along axis of boiling lion. 1. By plane of ehuUition^ an expression frequently to be used, I refer merely to the mean surface of the agitated liquid. Above this there is a similar well defined plane of condensation, and the zone of constant temperature lies between these planes, nearer the lower. The data taken as a whole show that for l^'" or 2'™ above the plane of ebullition the variation of temperature is not more than two or three degrees from the boiling point. These changes are produced by rela- tively great diflerences in the intensity of ebullition. The use of thick asbestos jackets increases the height of the space of constant temx)era- ture. As was the case with mercury, the zone of ebullition is sharply marked both above and below the surface of the liquid, and its height dei)ends very materially on the violence of the boiling. The tube dur- ing ebullition is apt to be very dark brown, so that it is sometimes diffi- cult to discern the boiling surface at all. It is well, therefore, to mark its position beforehand. Taking the above results as a whole, itap- )>ear8 that just Jibove the Surface of ebullition the temperature is con- stant for an indefinite period of time, and that it does not differ from the boiling point of sulphur more* than a degree at most. Ejqiloration for constancy of temperature; zinc. — In Table 15 I give (702) BABUB.] CALIBRATION OF ELECTRICAL PYROMETERS. 109 similar observations relative to the constancy of temperature along the axis of a zinc crucible. The form with open tube, Fig. 15, is used, so that the variation of temperature aloug as much as 14*^'" of the axis can l)e measured. During measurement the central tube is closed above with a loose plug of asbestos wicking. Exi)eriments are made with two furnaces, placed side bj side and heated simultaneously. It is difficult to define the surface of ebullition with reference 'to the crucible, for the zinc 18 apt to bo porous and of great bulk, and it is sure to be spattered against the top of the crucible and to solidify there. T in Table 15 is approximate, since the variation of T is alone of interest here. It was necessary to finish the observations for the first crucible before com- mencing those of the second. Table 15. — Constancy of temperature alonj the axin of the zinc a'ucible. Form, cf. Fig. 15 yUKXACE No. 1. Ileitflil above IhlttOTIl of crucible. Cm. 4 8 10 12 8 4 °C. , 21.6 I 21.0 I 21.6 j 21.6 I 21.6 I 21.6 ' 0n. I i Microvolts, j I1<«0 I 11060 I 10950 i 10670 ', HOIK) I 11000 I T. o a. Time. Ilourt. 3.18 3.30 3. 33 3.38 .3.43 KemarkH. Liquid Hurfaco about 8^' above bottom. FUKXACK Xo. 2. 4 8 10 IJ 14 10 8 4 21. 21.6 21.6 21.0 21. G 2-. a 21.0 21.9 11040 11060 110(0 lliOTO 10830 11090 11080 11U80 3.. 55 ' 3.58 3.67 3.70 3.77 3.K5 3.9'J 4.00 Liquid flurf:i(;o about 8<^' above bottom. To obtain a full understanding of the purport of these data it is neces- sary to turn to Fig. 15, p. 94, where the positions of the present points oi* observation have been marked with little circles. The data, there- fore, show most remarkable and unexpected constancy, particularly so when compared with the results for mercury and sulphur. This is due to the fact that the distilled zinc condenses on the sides of the upper and colder parts of the crucible and then runs down ou the walls — a fact well demonstrated by breakage of the crucible after the experi- ment. Hence the interior is jmictically encased in an envelope of boil- ing zinc, although the exterior of the crucible by actual measurement shows 1,40(P aiMl more. A significant result of these explorations is this, that the ])assago from the region of boiling liquid into the region of vaporized zinc is not discernible in the data. Temperature is prac- tically constant until the upper cold parts of the crucible are reached, (703) 110 MEASUREMENT OF HIGH TEMPERATURES. [BULL. 54- PRACTICAL CALIBRATION. Investigation of data. — Instead of extending these experiments into higher temperatares and determining further data for the fire-clay ap- paratus, it will be expedient to actually calibrate a series of elements* Such experiments will show both the constancy of the divers boiling points as regards time, as well as their absolute correctness as com- pared with the data of Chapter I. Indeed, the degree of identity ex- hibited by distinct series of data obtained almost a year apart, by thoroughly different methods and under different circumstances in all other respects, will be the best available criterion of the validity of the said series of results. Hence the fallowing table is given with consider- able fullness. The boiling points taken are zinc (930^), sulphur (448^), mercury (3570), aniline (measured 187o), and water. All observations are made in time series ; and for the temperatures t and T of the cold and hot junctions, the electromotive force e microvolts was observed at the time s[>ecified on the same horizontal row. . The mean of these isolated observations being tiiken, the results arc used for the calculation of the constants a and b in equation (1) above, by the method of least squares; a and b are inserted in the ninth column. The fifth contains the cal- culated value of 6, and its difference from observed e is given in the sixth column. Finally, in the seventh and eighth columns are inserted the correction C20— « J^nd the value d. B e. en—c. €»: Micro. 4f toU*. Micro volU. Micro- volUi. 9354 —174 9 Mirro- voUm. 9101 0185 9170 0175 0170 0150 0183 0182 9227 9228 9229 9229 0229 0190 a and 6. Microvolts. 8.U49 0. 002357 Time. (7(M) h. fit. 2 24 27J 3 00 7 33 38 4 2 15 40 4^ 50 55 5.2 12 Mean 12 48 18.8 90.0 633.6 660 -35 -0.3 624.3 From the coDStants contained in these tables I bnve calcniated the values of fao when the difference of temperature varies between T— 20= lOOo, and T— 20=l,500o, for the reason that I shall make use of these values below. In general there are three sets of valu'es of e^ available ; the first of these is calculated with the constants, including the zinc calibration ; the second with the constants applying only as far as the sulphur calibration contained in this chapter; and the third with the constants applying as far as the mercury calibration contained in Chap- ter I. The last two sets having been made respectively in Washington and in New Haven will be so designated. To these couples are added results for Nos. 19 and 20, both of which are 5 per cent. Ptir alloys. They will be referred to elsewhere. Bull. 54 8 (767) 114 MEASUREMENT OF HIGH TEMPERATURES. [BULL. 54^ Table 17. — Valtiea ofe^ in mxcrovolU, WASHINGTON AND NEW HAVEN. No. 17,«Ms No. 18,eM = No. 22, ew = r-«. With sine. Washing- ton. 838 1723 2656 36to 4061 5734 6865 8023 9238 10600 11809 13166 14569 16020 17617 Without sine With sine. Waahing- tOD. Without zinc. With zinc. Without zinc Washing- ton. 821 1719 2696 3751 4883 6094 7383 8749 10194 11718 13319 14998 16755 18589 20602 New Ha von. WaHhing- ton. New Haven. Washing- ton. Washing- ton. Now Havon. 100 200 300 400 600 600 700 800 900 1000 1100 1200 13C0 1400 1500 815 1707 2677 .3726 4852 6056 7339 8700 10137 11654 13249 14921 16672 18500 20407 830 17C8 2632 8603 4620 6687 6099 79.V 9165 10419 11719 13067 14462 16903 17391 816 1704 2666 3702 4811 6994 7250 8580 9983 11460 1301U 14634 16331 18102 19946 813 1704 2671 3761 4836 6034 7309 8561 10001 11590 13179 14839 16676 18390 20281 833 1716 2644 3621 4646 5721 6843 8013 9232 10497 11812 13176 14587 10045 175.53 817 1711 2680 8726 4848 6046 7319 8670 10096 11598 13177 14831 16562 19185 20252 814 1707 2679 3729 4857 6066 7350 8714 10167 11878 13278 11956 16714 1^548 20463 WASHINGTON. No. 36, 6to = Without No. 3b, ew = With ziuc. Without zinc. 833 1745 2734 .3801 I 4948 : 6154 7470 8825 10316 11855 13470 15165 16036 18789 20698 Nos. 19, 20, cxo = With zinc. 807 1739 2708 3982 5254 6729 8291 9980 11792 13732 15808 17988 20307 22749 25319 Without zinc. 297 6(H) 906 1218 1533 1852 2177 2506 2840 3178 : 3520 3868 a:=2.944 b =0.000256 (a=3. 065) (b=-0.0U0()93) I 305 609 910 1210 ^•^)7 1803 'J0U7 2389 2678 2908 3-54 3539 Di8cu88ion of data. — The most satisfactory method of discussing the results of Table 17 will consist in first mapping out its data graphically, and inserting upon the loci so drawn those results of Table 16 which are the immediate conseqi.ences of experiment. I will first consider a comparison of the results of Chapter I and of Chapter II for such cases in which the calibration was carried forward about as far as 400^, the (768) ■%• . m BO Fio. 21. Chart showing the relation of \ ■i I , ^ . t ' ■ J" I . ■> *■ V ' ♦» 7, ■ ^ t -I .- / '. /■ ii-. .' ' ■ '■"■'"■'■ !'. f*th f i»' •■- »■ ' 5*- ■ i f ..: ■ '. A S-.. * J -•• f.* '■ *■> *'. . L** ^V- « Kt jfic;: ► '^*' ■ ■ i3 "^ ' f njnM' . *".'■' .1 X.i .J • •■«■>. . ■ I ■ «■ . "^ .1 »>*;• L..f :•;■■ ■ ; Si'-- ■■ o ■■ 1 f ■- F" / 1 '_ !^'-.- -''■-. ■ I*. .■ p * ^ 1 ' . '.I - ' ffi . » ■< f* :'•■:': • ».».' ■ . , BABU8.J CALIBRATION OP ELECTRICAL PYROMETERS. 115 constants then calcnlated from these data and used for trial extrapo- lations. It appears from this comparison that the resalts of these trials are almost perfectly coincident. In case of I^o. 17 the difference at 1,5000 is only 49; in case of No. 18, 140; in case of No. 22, 9o. Now, when it is remembered that the results of Chapter I are obtained by the large vapor apparatus there described and that the results of this chapter are obtained by the small practical forms, the coincidence of the results of this exceedingly severe test is most remarkable and gratifying. In Table 16, moreover, the relatively small differences be- tween the parenthetical results for observed and calculated e, is further evidence in favor of the statement just made. If, however, we include the boiling point of zinc in the present com- parisons and derive the constants by the method of least squares, the relatively large differences thus obtained at once show that the quad- ratic equation assumed is no longer applicable, so far as the results in hand are concerned. The loci corresi)onding to these new constants differ at 1,500^ by amounts as follows: In case of No. 17, by 126^; in case of No. 18, by 116°; in case of No. 22, by 119^; in case of No. 35, by 1260; in case of No. 36, by 130°. Similarly the differences between observed and calcnlated e in Table 16 (without parentheses), differ by large values. To obtain a notion of the nature of this difference it is well to insert the observed result for zinc in the chart, Figs. 21 and 22. When this is done it appears that the position of the zinc point bears no observable relations to the positions of the sulphur, mercury, aniline, and water points. There are three causes for this large discrepancy to be considered: 1. Either the relation between temperature and electro- motive force in case of platinum-iridium elements is circumflexed or anomalous between 500^ and 1,000^; or the accepted value of the boil- ing point of zinc, 930^, is too large by about 75^; or the boiling point of zinc in the crucible calibration has not been reached. The last of these suppositions is easily disproved, both by the fact that during ebullition zinc dust escapes from the top of the crucible, and that after breaking the cold crucible the evidences of ebullition are apparent in drops of zinc scattered against the walls and solidified there after cool- ing. Again, the temperature on the outside of the crucible must have been at least 600° above the boiling point of zinc. Finally there is an almost complete coincidence between the zinc data for the large cruci- bles, in Chapter I, and the present data for small crucibles, as wjU ])resently be shown more at length. Hence the source of the zinc dis- crepancy in question is to be referred to one of two causes: either the platinum-iridium thermo-couple shows a circumflex- like anomaly in the relation between electromotive force and temperature between 500^ and 1,0000, or tiie values heretofore assumed for the boiling point of zinc [ca. 930^) are too high b 75^. To decide between these two difii- culties, the importance of which is here regarded merely from the (709) 116 M£ASUR£li£NT OF HIGH TEMPERATURES. [bijll.64. standpoint of the present investigation, is not the purpose of the present chapter and will be touched upon later. Time variations of thermo-electric data. — In this place a consideration of the degree of coincidence between present and former zinc data is per- tinent. In the results given in Table 6, Ghaper I (p. 78, June II). the values for the boiling point of ziuc if expressed in (reduced) units of elctromotive force were: MkrovolU, No. 17 e2o = 9220 No. 18 f2o = 0180 (188) No. 22 €go = 9240 These values are available for comparison with the data of Table IG, Chapter II, from which the corresponding mean values are found to be : Microvolts, No. 17 «2o = 9190 No. 18 €yo = 9l40 (188) No. 22 ejo = 9200 This slight difference of less than ^ per cent in the values of e2o« and which amounts to only about 3^ of temperature, is quite negligible and easily referable to the incidental errors of experiment. In the large furnaces of Chapter I such an error is possible, even at the cold junction. Duration of continued ebullition j constant high temperatures. — This brings me finally to a consideration of the constancy of Che boiling point as observed with the crucibles described, when this constancy is con- sidered with reference to the time during which ebullition has been going on. A series of such results are given in Table 16, and if neces- sary others may be supplied during the course of the discussion. Turn- ing first to the results, e^y for zinc, it appears that after the value of T has become constant at about 3 o'clock, the variation in e^o from this time until 5 o'clock (9 180 microvolts to 9230 microvolts) are only a little more than ^ per cent, of e^, corresponding to about 4^ centigrade for the two hours of ebullition. This variation is an almost regular in- crease of T. This strikingly perfect degree of constancy of the teni- I)erature of this crucible is additionally attested by the values of Czo for the elements Nos. 18, 22, 35, 36, to which I might add many other results, were it at all necessary to supply further corroboration. By way of illustration, merely, I will give a few data obtained when the contents of the crucibles are antimony or bismuth instead of zinc 1 will also add some results derived from commercial cadmium. In the case of bismuth the walls of the cold crucible, after boiling, were lined above the surface of the metal with a fine granular coating of bismuth, and very near the surface a narrow zone of little bismuth beads was appa- rent. Nevertheless, ebullition can only have commenced, as is proved by the thermo-electric data, and the incrustation is due to volatilizatiou (770) t 19000 12000 1 1000 aooo safi fififii «Y' aq I ( I ! ' 1 » » ■ I ' / 1 I . %. Fio. 22. Chart showing the rt N K .,■ i >• • . . . t I k ■■■ I "^V ■ \ :" . 1 H \ ■f ■ * . !- i V ' 4' •, ■ *,■ fv-- ^■' ■.'' M&D*.) CALIBBATION OF ELECTRICAL PTS0HETEB8 117 below the boiling point. The temperature in tbe oases of both bismuth and antimony was sufflcientlf high to iiartially fuse the porcelain in- sulator, and to cause it to stick fast iu tbe central tnbe. This is a great annoyance, because platinum at high white beats has only small tensile strength, and is therefore easily pulled apart in the endeavor to withdraw the element from tbe tube. Tbe difficulty is obviated by nsing fire-clay insulators. Tabu l.B.—a-ueiMe, Fig. 13, ckargtd «ci(fc KmvM. The crucible after the last uieasuremeiit, being fluxed through, began to leak, putting an eud to tbe experiment. The value o£ T would of course only be approximate if ubtaiueil by using the zinc constants of Table 16 for extrapolation. Nevertheless; the continued rapid increase of temperature, T, shows that the boiling point has as yet by no means been reached. The behavior is therefore in striking contrast to the zinc. charged crucible. Tabi^ 19.— Cnicibh, Fig. 13, charged vUh anOmonf. No. .. .. ... |t,.„ Jfim,. U^TO.^. " a =oiu «*.. A. m. 50 ; 12110 IMIO D41 17 M 12730 1273U 45 17 K ; laTlW ISTBO 48 17 10 1 I!^ I2m 4B Elemanl No. 17 pollttl kpirt no wUhilrB-tas it, No. IB ■ubaLi- totflJ for It. IB ^2 llaiO < 12830 7SS IB 33 IS210 ; i3a3fl SO IB 1B 13210 13:30 33 133M I34W W is S3 40 IS M 13BM is«o 4> Here the remarks already made under bismuth nearly apply. The craoible leaked after the last observation, and the experiment had there- (771) 118 MEASUREMENT OP HIGH TEMPERATURES- (BUIJ.5i. fore to be discontinncd. T wonid have the approximate signification stated. The porcelain tubes again soften. In operating upon cadiniuui, I first tried glass tubes. Bat after many trials the experiment was abandoned, both because of the decidedly re- duced viscosity of glass at low red heat, and because the simple ring bnrner, even while a powerful pair of bellows is used to intensify the blasty is not capable of easily boiling cadmium. Hence the clay cruci- bles were nsed and results were obtained as follows. The value of Tis here appended, as derived from Tabic 16, both for the case in which the exterpolation is made with zinc, and as made without zinc. The cad- mium nsed is of commercial purity only. What I aim at here is a mere illustration of method. Table 20. — Crucihle^ Fig, 13, ckt^rged with cadmium. ^0. t. e. e». Time. Cum zinc Sine ziut T. T. m OC. Micro- VOltM. Micro- voltt. h. fn. °a oa 17 21.2 7568 7577 12 38 783 734 17 22.8 7626 7648 1 790 740 17 23.8 7558 7588 18 783 735 18 21. « 7541 . 7553 12 43 785 743 18 22.9 7528 7550 1 3 785 743 22 21.9 7568 ' 7583 12 47 784 740 22 23.1 7577 7601 1 6 785 742 36 22.2 8346 8363 12 52 785 726 35 23.2 8:«7 8362 1 10 785 725 36 22.5 8333 8352 12 55 784 724 3« 23.5 8325 8352 1 12 784 7M The results are given here chiefly by way of contrast with the above tables for bismuth and antimony, since they show an admirable de- gree of constant temperature maintained for nearly one hour at a relatively low temperature. Inasmuch as the interval between 60(P and 1,0000, if the assumed boiling point of zinc be correct, is anomalous and not simply quadratic, the interpolation here made for the measure- ment of T is unsafe. Hence I have given T both a« exterpolated from calibrations ((P to 450^) excluding zinc, and as interpolated from cali- brations including zinc. If there were no anomaly the constancy of the values of T found by operating with divers elements would make these resulto very trustworthy. I have made other similar experiments with selenium and with zinc chloride ; but respecting all of these the remarks made for cadmium apply. Further data are therefore omitted here. Duration of continuous ebullition^ low temperatures. — Returning from this digression, I will next exhibit the constancy of temperature for the . (772) BABUB.] CALIBRATION OP ELECTRICAL PYROMETERS. 119 time series of boiling-point experiments made in the glass boiling tabes. The data of Table 16 are again available with a few supplementary results to be inserted below. The variation of temperature during about an hour's uninterrupte Not taken. . 2631 * 300 12<'" above surface of liquid (melted HgCls). In vapor. 2631 300 0^ above surface of liquid. In vapor. 2647 803 ■ 0** above surface of liquid. 36 Saocinic acid . . . 20M 255 1 ! ( The acid boil» brown, t. e,, chars and goma 2088 255 1 .*. boiling point rises rapidly. 2104 256 'Not taken. > 2240 270 Ebullition intensified. 2300 276 1 J. — ' Liquid very dark brown. 86 Naphthaline.... 1741 210 1 n, m. ' 1 45 1 Boils well and clear; combastion tuba ele- 1606 205 55 raent 2^" above surface of liquid. Very 1696 205 2 distinct planes of demarkation. 1601 205 • ■ 8 1670 204 : 15 1692 205 20 1730 209 56 More naphthaline added. This obrionaly 1730 2C9 57 changes the composition of the mass and the boiling point. 36 Pyrogallic acid.. 1818 218 No constancy of temperature. DeoompoMd, forming a viacona mass. (774) BABUl.) CALIBRATION OP ELECTRICAL PYROMETERS. 121 Table 22. — Available aubtfanoes far hailing point erperimenta^Contiiiued. 3$ Bensoic add. 86 Oamphor Micro- 9oUs. 1781 1 0. 909 2on 254 2071 251 2071 264 2071 254 2077 265 2077 255 1632 208 1638 210 1638 210 1645 211 1648 211 1642 211 1640 211 1634 210 16U 211 225 30 37 45 3 25 85 4 15 20 46 5 15 85 6 6 6 Bemarks. Boilii qaietly; perhaps more so thannaphthap line. Boils quietly. Preferable to bensoic acid. Scarcely changen ooIqt* Inodorous. DlHtancift between planes of dcmarliation = 12«*". AHbeMoi* Jacket even red hot at one point. — > Jnst below upper plane of deroarication.. — > Just above lower plane of deuiai kation. Data for the variation of boiling poii|t with pressure with a special view to thermometric application have been investigated for naphthaline (218^) and benzophenol (306^) by Crafts.^ The possibility of lisiag selon- iuin in glass boiling tubes has been demonstrated by Troost.* V. Meyer^ has made ase of amylbenzoate, diplienylamiu, and phosphorons penta* sulphide. Volatilizing points. — In addition to the experiments on boiling points, I made an attempt to utilize the above apparatus for measuring points ot volatilization. Professor F. W. Clarke suggested the arsenic point as a desirable and insufficiently known datum and Mr. O. F. Becker made a special request for the point of volatilization of cinnabar. With both of these substances as well as with sal ammoniac I made large numbers of experiments, but failed in getting satisfactorily constant and reliable re- sults. The efifect of applying the ring burner around the sublimable solid in the tube is to form a very perfect hyperboloid of one nap, as it were ; a figure, in other words, which resembles in form a united stalactite and stalagmite. The effect of heating is to volatilize the solid around the plane of the ring burner, and condensation takes place above and below the plane, forming the figure specified. A priori, it might be argued that so long as the hyperboloid remains intact and completely envelops the thermoelement, so long will the temperature of the junction not increase above the point of sublimation of the substance. Except in » Crafts, Chem. Bar., vol. 20, 1S87. p. 709. *Troo8t, C. R., vol. 95, 188^2, p. 30. •Goldaohmidt a. Meyer; Chem. Ber., 1882, voL io, p. 137, (776) I. £• I 5 f .1' ; ii: III ■'!; i> ' il I 'I I" I I . ■ :i !|- ■.■ P i I' J ■ I- *! !'■■ — i2ti MEASUREMENT OF HIGH TEMPERATURES. [BUtL.64. the ca^e of U4NCI, in which sublimation is very rapid, I was not able by using the tubes to obtain very distinct points of sublimation, show- ing an unmistakable tendency of these substances to superheat, or at least to contain superheated vapor in the interstices of the mass. Arsenic, for "instance, forms a distinct mirror on the tube before any constancy of temperature is reached, and, moreover, the temperature may be increased above this point almost to the limits of heating capacity of the burner. In the case of cinnabar the conditions are still further complicated by the tendency of this substance to decompose in air at high temperatures. It is necessary, therefore, to pass through the tube a current of carbonic acid. By doing so, however, the tend, ency to irregularities of thermal constancy are much increased. For the reasons stated I think it preferable to withhold my data from this chapter altogether, and to publish them in connection with certain ex- periments on the relation between boiling point and pressure which I have in view. For such experiments the above apparatus. Fig. 11, is eminently fie. Possibly if the given substances be under sufficient pressure to liquefy them at the subliming point, a true value for the tern, perature of ebullition mtij be found. Subsidiary dat^. — In conclusion I desire to insert here a number of subsequent results, the electro-motive force of which is given on a dif- erent scale from that heretofore adopted. These data are not to be put in relation with the results given above, but are subsidiary as regards the matter discussed in Chapter lY, on which they have an important bearing. In each case the apparatus used to obtain them has been the perfected form, and the results are therefore as trustworthy as my methods can make them. Allowing for the difiference in the assumed value of the standards used, they agree with such results as have al- ready been given, with all desirable nicety. Table 23. — Calibratian in zinc rapor, December 10, 1886. [Charge of cmciblB, onnces.] No. e. e. en. Time. Mean e», 37,38.39,40. 0. Micro- volts. Micro- volts. h. m. Microvolts. 22 20 0830 9830 2 15 11033 35 21 11070 11078 20 36 22 10980 10997 25 37 23 11010 11036 30 22 24 9780 9814 35 3d 25 10980 11023 37 39 26 10980 11031 40 40 27 10980 11040 45 22 28 9735 9803 55 22 28 9780 9848 3 00 The following results were obtained at a later date. The thermo- couples are tested in three different furnaces, placed side by side and (776) BA&U8.] CALIBRATION OP ELECTRICAL PYROMETERS. 123 heated at the same time to different degrees of redness. The mean tem- perature of the outside of crucible was measured and found to be 1,4000. Table 24. — Calibration in zinc vapor, November 10, 1887. No. 37,38.30,40. Oonple No. t. tf. «so. Time. OC. Micro- voUi. Micro- volts. h. m. 37 20.8 11065 11070 1 40 37 21.2 11065 11070 1 60 37 22.8 11050 11070 2 5 38 23.6 10095 11030 2 14 38 24.0 11013 11050 2 20 88 24.8 11030 11070 2 30 39 25.3 11040 11080 2 40 39 26.0 11075 11130 2 45 39 26.6 11030 11090 2 50 40 27.0 10995 11050 2 55 22 27.3 0883 1 9950 3 1 2 3 1 2 3 1 2 3 3 3 MierovoUt. 11074 Table f&.^Calibration in tin. No. 22 35 22 22 22 36 37 t. e. 1 1 °a Micro- i volts. 20 I 15630 ; 21 18460 21 15860 22 15300 23 16100 24 18050 25 18950 , 1 et«. \ Time. 1 Micro- ^ volts. h. m. 15630 6 30 18468 • 35 15868 40 15317 40 16126 40 18984 50 18993 55 An accident here stopped the experiment at intense whitie heat. It has been stated that a thick, viscous slag soon forms over the surface of the tin and the walls of the crucible, wholly enveloping the metal within it. A criterion for the boiling point of tin, therefore, will con- tinue to be difficult of determination. Tablr 26. — Calibration in bismuth. No. t. OC. 22 20 22 20 22 20 22 20 22 20 22 20 22 20 22 20 22 20 i 22 20 1 1 e. f». Micro- volts. 11790 12620 13940 14800 15780 16380 16510 16630 15550 16900 Micro- volts. 11790 12620 13940 14800 15780 16380 ' 16510 j 16630 i l.'>550 I 10900 I Time. h. m. 6 5 15 25 30 35 40 45 50 65 (777) 124 HEASnBEHENT OF HIQH TEUPEBATUBES. [■inx.5i. This is Tory nearly tfae electric (latQm for the boiling point of bismatbt at least globules of bismuth are scattered around the walU of the cniei- ble. The bismath elag is not so dark and opaqae as the antimony slag, indeed, often quite colorless. Table 2J.—CalibratiOH in antimmg. So. t .. 1 «. Tim. a 1 Jliero- UilTV- W 1 lB-!00 > ISWO M ! ItODO lOWO » ' i8oa» isooo h. m. « 10 IS 20 35 In these experiments intense white heats are produced by firing the furnace with two parallel blast burners, apposite in direction so as to blow a Tortex ot Same in the furnace. The crucible is Qually corroded through, the antimony forming a corrosive ojiaque glaze with the clay of the crncible. A few small globules up as high as the ^t lid of the crucible (Pig. 14) indicated very approximate ebullition. Many other esperinienttj of the same class were made, in all of which the intejiseat degrees of white heat obtainable in the furnace (Fig. 14) were applied. Two aud even three injectore were inserted, the blasts for which were fur- nished by a large bellows of Fletcher's puttern, run 3 by a one borse power gaa-engioe. Tbe data are snb- ^ servient to tbe investigation in Chapter IV, where ^ the attempt is made to calibrate tbe thermo-couple ^ by direct comi>arison with the gas-thermometer. In a place, however, it is well to remark that definite data on tbe boiling point of autimony, bismath, lead, tin, etc., will probably not be attaiuable by such a method as the present, except by beating these snb> stances intensely in vacuo. Such experiments I hope to make at an early date, using for tils pur- pose the form of crucible. Fig. 14a, which can be hermetically sealed. (See Preface, page 22.) Thermo-electric datum for the melting point of plati- num. — Finally, it is interesting to contrastthese high* temperature data with tbe values obtained when the junction of tbe pbilinnm platinum iridium thermo- couple is heated by tbe o^ybydrogen blowpipe to extreme degrees of fusion. It is necessary for this purpose to make a tliemio conple of very thick wires T\a.'a. Apparatnafnr Olid to insulate ihpui by aid uf tubes of caiirined mjWng-poiBt of pi» |jujg_ jjj j,-jg_ 2:j ii convenient method of experiment (778) BABUS.] CALIBRATION 0£ ELECTRICAL PYROMETERS. 125 is shown. A A xbb, block of lime into which two capillary holes have been drilled, just large enongh to receive the wires /3 and y of the thermo-couple. These are united above by a little button of platinum lying at the base of a spherical cavity in the block A A. Bis an oxy- hydrogen blowpipe by which the button is fused. A lid of calcined lime similar to the block A A in form but having a lateral outlet oppo- site B may be added. But the ignition is intense enough without this. In the following table are given the values for e» obtained by heating the button in the open hearth, Fig. 23. The thermo-couple is old So. 18, the wires of which have been fused and drawn over again. Tablb 28. — Tkermo-electric datum for temperatures above the melting point of platinu.n. No. t. ew. Time. oO. Micro- voltt. h. m. 18 20 20400 1 48 20 20000 € 50 20 20400 8 00 20 20000 5 33 20 20400 50 Remarks. First experiment. ^Stfoond exiMriment. Fresh ^ block of lime. S Third experiment. Fresh bloik of lime. The curiously constant electrical result for the temperature of the oxyhydrogen flame under the given circumstances is remarkable. It is interesting to note that when by any accident metallic connection is broken, there at once appear violent polarization disturbances. This shows that at the temperature of the OQ^ blowpipe, lime is quite a good conductor of electricity, for it is less probable that under the given conditions conduction should take place through the hot gases. The thermal equivalent of the value of e in hand, however, is only 1,600^, a datum ceitaiuly too small by 200o or more. This small value is significant.^ It is in accordance with the small thermal datum for the boiling point of zinc, calculated from thermo-electric data, which apply only for the interval 0° to 400^ (cf. p. IIG). Hence it appears that the (*quation e:=ar+bT lAtiuum alloys obtained in Paris could be fused over without producing any serious variation of constants, and since I inferred from the researches of Devillo and Troost that the intense heating of platinum on a lime hearth before the oxyhydrogen blow-pipe, was itself a sufficient method of purification so far as the elimination of volatile and oxydizable con- stituents is concerned. Moreover, it has been stated in Chapter I that the general plan of work was to be such that special stress might be put on the efi'ect of vanishing quantities of an alloying metal added to phitinum. Hence I looked principally to obtaining a metallic body for the alloys showing fixed properties before and after melting. In the course of the investigation, however, it became painfully ob- vious that the labor of making the alloys, the fusions, rolling and wire drawing, the experimental evaluation and the computation of the con- stants had been very much underrated. I found, in other words, after about one-half of my investigation bad been completed, that the amount of work expended could have been justified only if the work had been 126 (780) BABUi.) ^ PYEO-ELECTRIC PKOPEBTIES OF ALLOYS. 127 begun with absolately pure materials. I found, too, that the purity tests which had originally been made were not rigorously sufficient ; that portions of the single wire of platinum lying far apart differed more seriously in their electrics than I had apprehended, and that the platinum itself when exposed before the oxyhydrogen blow-pipe during long intervals of time (several hours) showed very measurable changes of the constants which had originally characterized it, and must there- fore have changed somewhat in composition. An exhibit of the numeri- cal values of all discrepancies here involved will be given in the course of the chapter. When so large a part of the investigation had been completed, how- ever, it seemed expedient to push it to a close; for the classification diagram of the platinum alloys, which I was desirous of evolving, could not lead to serious misapprehension if only the scale of representation be chosen sufficiently small ; if the profile, in other words,, were reduced to a sufficiently small scale to make the errors negligible. Indeed, this appeared desirable because no general study of the electrics of the pla- tinum alloys as complete as my own has as yet been made. Again, since in the scheme of fusing 2 per cent, 5 per cent, and 10 per cent, alloys, it was customary to use consecutive lengths of the platinum wire, the results at least show the effect of alloying a specified metal to a given body of platinum. Finally, the plan of operation by which the work was done is worthy of description, and with the amount of expe- rience gained in x)rosecuting this tedious research I will, at an early opportunity, be able to repeat the work and bring the constants fully up to the standard of accuracy desired ; in other words, to make the chemical measurement compatible with the electrical measurements. Despite the discrepancies mentioned, this chapter is not barren in special results; and perhaps my main motive in publishing the data is due to the fact that they lead to a relation between the electrical con- ductivity of platinum alloys and the temperature coefficient of that conductivity, which is so nearly independent of the (alloyed) composi- tion of the metals that I feel urged to ascribe to it the importance of a law. Very clearly does this appear when the present results for alloyed platinum are compared with a series of corresponding results long since found by Dr. Strouhal and myself when working with steel. I fully believe that in endeavoring to explain the mechanism of electrical re- sistance, the law in question will be more fruitful in suggestions than any allied phenomenon which has yet been investigated. Inasmuch as fused platinum appears to be the universal solvent for metals, the incontestable importance of series of data such as I here endeavor to investigate is more obvious in proportion as the number of metallic combinations obtainable is larger. To recapitulate, therefore, the law in question (T use the term "law^ simply to I'iicilitate exprc\ssion) is iiulc^jiendent of the ingredients of the alloy except in so far as they modify its electrical conductivity. AUoy- (781) 128 MEASUBEMENT OF HIQH TEMPERATURES. tnu^H. • ing is here merely a method of modifying resistance, and the lesalts are studied with reganl to the resistance prodaced, not with regard to the way in which resistance is modified, in all of this work the chief object is to get nearer the trae nature of electrical resistance, as a means possibly subsidiary to arriving at some results relative to the nature of electricity itself. FUSION Am) MECHANICAL TREATMENT OF THE ALLOTS. * Fusiouj rolling. — It has just been stated that it was my purpose to obtain groups of 2 per cent., 5 per cent., and 10 per cent, platinum alloys of as many metals as possible. The qnantities were therefore weighed out in proper proportion and fused on a lime hearth, before the oxyhydrogeu blow-[)ipe. The blowpipe is identical with the one described in the next chapter. The heartbs consisted of cubes or rect- angular solids, cut with a hack saw from a large lump of lime as free from fissures as possible. Into each of the sidfs semicircular cavities were dug, with a semicircular faced drill, on the lathe. Kickel, gold copper, palladium, and tin were quietly absorbed by the melted plati num globule. Silver boiled perceptibly. Iron, and more particularly aluminium and manganese, were absorbed explosively. Chromium cobalt, and even iridium were apt to splutter. Zinc, molylnlenum, an timony, bismutb, lead, must be frequently added, but the quantity ab sorbed was usually sufficiently large to change the qualities of platinum perceptibly. With regard to rolling, it may be stated that the 10 [)er cent, gold and the 10 per cent, tin alloys are too brittle, and must there- fore be diluted with further amounts of platinum. In tbe same way 5 per cent, chromium, 5 per cent, aluminium, 10 per cent, copper, and 10 per cent, nickel alloys, and others, usually break on rolling. Cobalt alloy, moreover, a sorbs gas and inflates itself on cooling. Iron alloy, 10 percent., could be rolled b^' superficially fusing the rifts. This ex- pedient, tbough not rigorously in favor of homogeneity of comiH)S]tion, had to be frequently resorted to; for instance, in casrof antimony, bis- mutb, zinc, silver, and had alloys wbich are more or less porous after fusion. Curious properties seem to be possessed by the tin alloys, in- asmuch as tbe 10 per cent, alloy is brittle and hard enongh to scratch iron. Experiments were made in rolling hot ingots, but with doubtful success, tbe qnantities being too small to retain their heat for any length of time. I add, finally, tliat tbe work threw some light on the con- ditions of difi'iision of any liquid metal in any other liquid metal, a phenomenon as yet imperfectly known. Preliminary daia^ density, — In all about fifty-two alloys were fused to buttons. These were tben rolled to little bars of idatinum about lO*"" or more in length, and about 0.013 d*'"* in section. Alloys of this length and section are suitable tor preliminary measurements of resistance and density. Tbe data for density are given in Table 29. They were obtained by suspending the platinum rods from a fiber of silk in a long (782) BABUB.] FTBO-ELECTBIC PBOPEBTIES OF ALLOYS. 129 , Stand-glass of distilled water and making the cnstomory measorements. To make the process more convenient the left-hand scale-pan was re- placed by a special lateral arm, being virtually a bent lever, the weight of which was concentrated as near its lower end as practicable, in order that the platinnm rod might be hang as far from the center of figure or standard of the balance as possible. In this way abundant room for the stand-glass was easily secured. Measurements of density are sub- servient for the calculation of specific resistances, but they have an intrinsic value of their own. Table 29 contains the results of the density experiments. In it 2, g, and m refer to the length (<^'°), the section (d<»>), and the mass (g) of the bars of alloy. Jt ^nd Jo denote their densities at i? and Q^j respec^ ively. The alloys are usually arranged in series of increasing percent- ages of alloy, but where more than three alloys are examined these percentages must be inferred from the values of Jo* Special analysis of all t|he wires would be superfluous, for the reasons stated in the in- troduction. The results are intended to be purely physical. Table Q9,— Density of platinum alloy$. No. 1 1 2 2 8 8 4 4 5 5 8 7 7 8 8 • 10 10 u u 18 13 18 18 14 14 1» AUoy. PlAtinom ....do .........>.•..-. ....do ..•...•••••••>•> Gold ....do ..•...••>••••••.. ....do ....••-.....•*•-< ....do . . . .do .......>..••.•>• ....do ................ surer ....do ......••••....... ....do ...••.••... ....do ......•••....>... ....do ................. ....do PftUadinm ....do • ....do ..........••.•..• ....do ..............■.< ....do ................. ....do ................. Iridiam ....do .........•..•■••• ....do ....do ......•< ....do .........■••■...< ....do .....••......••.• Copper ....do .«••■•••••••.■•.< ....do ................. ...do m m § QO •■•>••• ••••• .... Ball.64 9 { q m t At A« 22.80 0.01288 5.9889 o 19.5 21.306 21.321 22.18 1187 5.6108 18.0 21.297 21. 8U 22.18 1187 6.6108 12.6 21.808 21.818 15.46 0.01333 4.3877 2ao 21.290 22.306 15.45 1835 4.38n 13.2 21.260 21.270 15.50 1343 4.4177 20.2 21.206 21.222 15.48 1315 4.^4177 5.6434 13.4 21.211 21.221 85.80 0746 13.4 21.128 21.138 85.82 0743 6.6433 20.8 21.191 21.207 15.22 0.01285 4.1344 2a3 21.138 21.154 16l23 1282 4. 1346 13.5 21.163 21.173 23.88 1268 6.3454 13.6 20.991 21.002 24.05 1265 6.3798 20.3 20.964 20.980 24.05 0750 3.5377 20.2 19.380 19.896 24.04 0758 3.5381 13.9 19.394 19. 405 16.66 0.01252 4.3754 13.5 20.975 20.985 16.65 1250 4.3754 18.8 21.016 21.027 16.10 1316 4.8491 ■ 14.0 20.523 20.534 16.11 1314 4.3492 13.7 20.535 20.546 17.60 1280 4.4809 18.9 19.892 19.903 17.60 1278 4.4810 14.2 19.904 19. 915 16.34 0.01265 4.3896 14.3 21.237 21.248 16.27 1265 4.8819 14.3 21.283 21.294 16.00 1288 4.3865 14.5 2L282 21.293 16.01 1289 4.3866 14.6 21.252 21.264 17.95 1280 4.8977 14.8 21.308 2L320 17.85 1282 4.8804 14.8 21.306 21. 318 15.95 0. 01315 4.3335 15^4 20.662 20.674 15.68 1317 4.2718 14.8 20.666 20.678 14.74 1298 3.9415 16.0 20.584 20.506 15.02 imi 3.0990 15.5 •JO. r>oi 20.604 17.32 1303 4.230; 15.8 i'.:07 ; A« Mean, 21. 315 21.288 21.221 2L172 21.163 20.991 19.400 2L006 20.540 19L909 21.271 21.279 2L319 20.676 20.600 (783) OF HIGH TEUPE&iTUBBS. ■DtHtity nf platinum allagt — Cootlnaed. 20.023 18.900 so.ws 19.935 IB. 323 la.OTa 1D.TS* 10.687 It.W a. Ill 31.107 20.934 21. OlS so.tsi 20. U7 1M.U7 (784) BABUI.] PYBO-ELECTRIC .PROPERTIES OP ALLOYS. 131 Table 29. — Denaity of platinum aUoysT-Continaed, No. 32 33 33 34 34 35 36 36 45 45 37 46 46 38 38 39 47 47 52 82 54 54 98 AUoy. Alaminiiiin . . UAnganese .. ....do ........ ....do ........ ....do ........ Molybdenum do ....do ........ do ....do ........ Lead . ...do ........ ....do ........ Antimony ... ....do ........ Bismuth ....do . . . • do ........ Zinc ....do ....do ........ ,...do . ....... Cadmium.... 12.00 n.44 n.44 14.35 14.34 12.87 14.36 14.36 13.76 13.76 16.86 14.58 14.57 17.14 17.14 13.47 15.02 15.08 18.33 13.84 12.29 12.28 12.22 1262 0.01296 1298 1287 1287 0.01320 1298 1296 1228 1225 0.01278 1212 1218 0.01343 1340 0.01311 1200 1202 a 01232 1228 1261 1262 1254 m 8.1388 3.0871 3.0872 3.5870 8.5867 3.6090 8.9585 3.9585 8.5869 8.5869 4. 5626 8.7537 8.7539 4.7703 4.7703 3.7898 3.8495 3.8495 3.2990 3.2988 3.2496 a 2496 8.2667 o 10.7 n.2 13.8 U.4 14.2 14.6 15.2 11.8 13.9 18.4 15.5 18.0 17.6 15.8 12.0 16.1 13.4 17.8 18.6 1&2 19.8 90.0 At 20. 715 20.814 20.779 19.412 19.434 2L250 2L239 21.260 21.298 21.281 21. 167 21.230 21.228 20.722 20.762 2L166 2L337 2L297 20.065 20. 114 20.950 2a 959 A» A« 20.724 20.823 20.790 19.421 19.445 2L263 2L252 21.270 2L809 21.295 2L180 2L240 21.242 20.735 20.772 21.179 21.847 21. 311 20.076 20.128 20.975 20.975 (2L 815)1 20.724 20.807 19.433 2L263 2L261 2L802 2M80 21.241 20.758 2L179 2L829 20.102 20.975 Preliminary data^ electrical resistance of rods. — Having given the valnesof Jo it is easy to measare the resistance of the bars of platinnm alloy by carefully applying Matthiessen and Hockin's^ or other similar method. The resistometer shown in Fig. 24, is so conveniently appli- cable that a short description may be given of it even if its principles be 'well known. The appar atus may be made unusually compact by using Kohlrausch's admirable form of Wheatstone's bridge. In practice it is conveniently inserted in the same circuit with the thermopile adjust- ment, and the two Daniells used as a source of current. All circuits are to be made momentarily, of course. In Fig. 24 the Kohlrausch bridge is shown at A. .B is the attach- ment for small resistances, D the standard with which they are to be compared. Let sshe the small platinum rod to be tested. It is firmly clamped down by the insulated levers m m, which properly insert it in the bridge circuits, m m and the similar levers nn, nn, may be moved along a stout horizontal rod at pleasure, and then clamped in any po- sition. Tbe part of ss to be electrically studied is stepped ofif by the rider 6, the points of contact of which are knife edges at a known dis- tance apart. The rider is also capable of being slid along a horizontal rod, parallel to the rod carrying nn^ etc. When in use e is held down >Cf. Maxwell: Electricity and Magnetism/M ed., 1881, p. 444. (785) 132 HEASUBEMENT OF HIOU TEHPEBATDSEI). by a aaitable spring. Ooe of these ridera (Fig. 26) is detached, and shown at r. In using Matthiessen and Hockin's method, it is merely nebeasary to connect Ofb, e,d, sncoessively with the galvaoometer. Ftos. H ud St. B«^Moni«tor with deUohed rider. Seals |. Table 30 contains the nnmerical reanlts investigated by aid of this appatatos. ft is the resistance {ohms) at the temperature t for t^ie sec- tion q ", and », the corresponding specific resistance (microhms). The length of rider indicates the efficient length of platinum rod for which any datum appTies. The value of «t in parenthesis refers to thin wire as oontainoed in Table 31. alloy t {thick wiret). [rider -lenKth 10,M.-.l So. Alloj. 1«78 2a 22 22 . '■ (.rf Ptatlnnm O.OllgT D.DIlgS 12S0 0.0t26S 1280 lS.2fl 1S.W 22.70 M.BO 21,40 23.m IS. 87 »S6 do ■ 34. 7S (780) BABOB.) PYRO-ELECTBIC PROPERTIES OP ALLOTS. 133 Tablk 30. — Electrical retittance of platinnm. alloyn {thick wires) — Continned. [ridor=lougth- 10.04«-. ] o. 13 14 ir» 48 Alloy. 1 ri 2397 2628 4899 2118 4531 1739 2110 2503 2879 8245 2680 3617 2004 2961 2946 5071 4685 2409 5025 3791 21C6 3294 8227 9652 1714 1942 2961 2001 1743 20.11 38.94 1273 1478 1438 1211 1457 2200 1223 1381 3894 1973 1191 t Copper... , 16 1 1 "^"»t'r~* ••»••.••..••••.•.••«••«••••••••••••...... ...do 17 ! ...do 1 17 . ...do 17 17 18 18 18 18 19 ao 16 15 20 20 20 18 18 17 17 21 21 21 15 21 20 20 20 19 17 17 16 16 15 16 16 18 19 15 14 22 18 49 - ...do ........ .•«..... ................... ........ 16 Nickel 17 ....do 18 ....do 19 Cobalt ?0 ....do - 21 ....do... 40 ....do... 41 ....do.... ?? 23 ....do 24 ....do 42 ...do 43 ....do ......................... ....V ••..... ...... 50 . ...do 51 ....do 25 Chromimn 2ft 27 .....do 44 ....do 28 Tin 20 30 ....do 31 Alamixifiim 32 ....do ........................................... 33 Manj^anese 34 do 85 36 ....do 45 37 Lead 46 88 Antimony 89 47 62 — do 64 do 68 ■•_ 9 ti ' (*.) 0.01815 31.51 81.92 1293 83.07 31.41 1308 C3.82 61.65 1216 95.09 90.18 188S 6&87 66.99 0.01261 91.93 2i.99 1804 ■ 27.51 27.87 1846 88.71 84.14 0.01261 80.01 80.40 1289 40.21 40.78 1290 84.88 85.28 1283 44.69 24.45 1218 0.01242 86.80 87.97 1276 87.67 88.06 1274 04.62 65.47 1209 65.65 56.60 1297 29.51 80.06 1982 61.70 69.86 1220 46.24 47.11 0.01314 28.47 2a 84 1268 • 4L76 42.30 1314 42.41 42.96 1210 82.06 82.67 0.01270 21.78 22.06 1337 26.97 26.30 1336 89.56 40.08 0.01233 24.68 26.00 1265 22.04 22.83 0.01298 26.11 26.45 1287 60.11 50.76 0.01320 16.79 17.01 1298 19.18 19.48 1228 17.61 17.94 0.01278 16.48 15.68 1212 17.68 laoi 0.01343 29.64 29.02 0.01811 16.04 16.26 1200 16.60 16.91 0.01232 47.84 48.74 0.01261 24.75 25.21 0.01254 15.0 EXPERIMENTAL DATA. Further mechanical treatment resistance of irire«.— Leaving the dis- cussion and comparison of these results for the text below, I may state that the experiments were continued by rolling and drawing down the wires in a wire-plate to a mean diameter of about .046<^°». With these dimensions, the wires were manifestlj^ well suited for a repetition of the resistance measurements just discussed under conditions thoroughly dif- (787) 134 MEASUREMENT OF HIGH TEMPERATURES. [BDLL.B1 ferent from the above. Id two respects, however, must the foUowiug results for specific resistance vary esseutially from the former results. During the process of drawing the wires down from the larger section (10«x 3= 12,000 D^"*) to the smaller section (10«xg= 1,200 D«°»), break- ages are not always avoidable nor even unfrequent; hence, it is neces- sary to refuse and to work the metal over thoroughly. Thus it happens that certain metallic constituents are partially volatilized. Again, the thin and thick wires can not be identical in homogeneity in the way called for by the present measurement unless the thick wires were themselves thoroughly homogeneous at the outset, a condition not to be premised. Hence the data of Table 31, the symbols of which have the same signification as in Table 30, will not be rigorously identical. The present data of resistance of thin wires are to be compared in the sequel with the thermo-electric and other data of the same wires. It is thus manifestly necessary to evaluate the respective constants of small lengths or parts of each of the wires. Inasmuch as all the data may be obtained accurately from less than 10^°^ of wire, and since for thermo- electric comparison only a mere point of this same partial length is nec- essary, it is obvious that the galvanic and thermo-electric constants may be obtained from a length of wire, the homogeneity of which may be assumed with impunity. For the total length being from 100*^" to 200*^ the ef&cient length is in every case less than one- tenth the length of the whole wire. It will be seen below that the stress I place on these re- sults is by no means superfluous. These remarks lead directly to Table 31. Tablb 31. — Electrical reinstance of platinum alloys (thin tnre«). No. Alloy. n t 9x10* ft Platinatn 12370 19 1257 15.65 • • • • do ••■•.•••...•••... ••■■.. .•.••••..... ..•..•.••••..*••.• 1 Gold 18300 15020 17380 18400 15450 22360 18170 14170 10490 13110 13740 15900 20C60 220€0 40330 15100 31520 14170 17470 19 19 19 22 22 22 22 22 22 22 22 22 21 21 20 23 • 23 22 22 1489 1452 uta 1400 1480 1548 1493 1620 1488 1534 1534 1520 1£02 1548 1570 1713 1700 1583 1570 19.13 2 22.88 3 ....do !.... 25.23 4 Silver 19.78 5 .... do •••••.............•.■*.••«•..■...■.••••■«•...•■.*.... 22.96 ....do 34.61 7 Palladium 19.67 8 ....do 21.54 9 ....do 24.86 10 Tridfiltn --TTT...... .XXX. ^..*x X .... ....... 20.11 11 12 ...do ! il.OT do 24.26 13 Copper ■ 82.27 14 do 34.00 15 48 49 ....do 63.56 ... do 25.98 do ..... 68.78 10 Nickel 22.44 17 ....do •.••.... 27.64 (788) BABUB.] PYRO-ELECTBIC PROPERTIES OP ALLOYS. 135 Table lU. — Electrical reaUttance of platinum alloys {thin wirc«) — Cuotinuecl. No. Alloy. n t gXlO* 1576 1576 1576 1500 1713 1676 1590 1500 1508 1676 1662 1785 1735 1500 1500 1610 ft' 18 Nickel 21180 18510 25560 10050 26400 14720 23130 26620 37710 37510 17600 34870 28770 17600 26030 82670 22 22 22 22 23 23 22 23 23 23 23 23 23 23 23 23 83.38 19 Cobalt 29.17 20 . •••GO .•••>*■.••«••••••••••.•.••■.■•..«..•••■..>••*.••..••• 40.29 21 ....do 31.72 40 ....do 45.24 41 ....do 24.68 22 Iron 36.78 23 ....do 42.38 24 do 60.28 42 . ...do ..................................................... 62.88 43 ....do - 20.89 50 60.51 51 ....do 40.91 25 27.00 28 do 4L30 27 52.90 44 ....do ......................... .......................... 28 13720 16090 24280 15700 18220 15000 20000 0700 11840 23 22 22 22 22 22 22 22 22 1610 1633 1662 1655 1655 1655 1647 1720 1662 22.21 29 do 26.27 30 40.35 31 AlnminiTim ., 25.98 8a 21.88 33 Maiig&Dotte. ........... .... . .X...X 26.31 84 40.25 85 MAIybdeDoiD 16.68 86 10.67 45 ....do -...,- ... 87 Load 8010 10510 17830 22 23 23 1720 1691 1601 15.37 46 do 17.76 38 30.14 30 Bismuth 47 0890 26340 14800 23 23 S3 1676 1601 1001 16.57 52 Zinc 44.55 54 25.17 63 Cadmiam A C ^ ing in all). ^ 710 ) 504 23 23 1810 2781 12.86 14.02 Thermo-electric8 of tcires. — Ilavinp^ obtained this table in the way described, the marked ends of the wires were next subjected to thermo- electric measurement by exposing them to temperatures lOOo, 358o, and 448^, respectively, in the boilin g tubes, already fully described in Chap- ter 11. The results are given i n Table 32. "Ifo.'' refers to the individ- ual wires of the couple examin ed, and gives the sign of the two metals thermo-electrically combined. Thus Auf+1— 0) denotes that the gold- alloy No. 1 is thermo-electrically positive to platinum No. 0. T and t are the temperatures of the thermo-electric junctions for which the electro-motive forces e (microvolts) apply, a and b the corresponding thermo-electric constants. Inasmuch as the thermo-electric data are necessarily most seriously affected by impurities in the alloys, it was (789) 136 MEASUREMENT OF HIGH TEMPERATURES [bull. 54. deemed fally snfficient to compute a and b from extreme valaes for f, T, e, and then to test this compatation with the intermediate valae. Laborious applications of the method of least squares were therefore discarded. * Tablb 32.— TA0rma-0{ecfHof of platinum aUoyn. No. 1 T e obserred. e CAlculAted. 10>Xa lO^Xb + 1-0 16 100 + 46 + 46 + 640 + 45 + 1-0 19 368 + 185 + 189 + 1-0 17 448 + 242 + 242 + 2-0 16 100 + 155 + 156 + 1812 + 263 Aa < + 2-0 19 356 + 637 + 648 + 2—0 18 448 + 832 + 832 + 3-0 17 100 221 221 + 2570 + 697 + 3-0 19 358 942 948 + 3-0 18 448 1225 1225 + 4—0 18 100 7 7 + 100 - 124 +. 4—0 19 358 6 18 + 4-0 18 448 18 18 + 6-0 18 100 32 82 + 436 - 412 A<5 + 6-0 22 358 88 94 + 6-0 18 448 106 105 + 6-0 18 100 107 107 + 1301 - 7 + 6-0 22 358 428 436 + 6-0 18 448 658 658 - 7+0 18 160 - 86 - 86 - 844 -1738 - 7+0 20 368 - 626 - 807 - 7+0 18 448 - 711 - 711 - 8+0 19 100 - 95 - 96 - 869 -2472 Pd <- 8+0 20 858 - 681 - 600 - 8+0 18 448 — 869 - 869 - 9+0 19 100 -- 120 - 120 - 1073 -3327 - »+0 20 358 -821 788 — 9+0 19 448 -1127 -1127 -10+0 10 100 ■-■ 222 - 222 - 2548 -1463 -10+0 18 358 -1066 -1052 -10+0 19 448 -1384 -1384 —11+0 19 100 - 386 - 336 - 3904 -1799 Ir -1-11+0 18 358 -1684 -1557 • -11+0 10 448 -2035 -2035 -12+0 10 100 - 617 — 517 - 5939 -3894 -12+0 18 358 —2480 -2453 -12+-0 19 448 -3228 -3228 r-18 + 18 100 - 15 - 15 - 77 -«I2 -18+0 18 358 - 271 - 257 —13+0 19 448 - 410 - 410 +14-0 18 100 + 44 + 44 + 1021 -4139 Cu -14+0 -14+0 18 20 358 448 - 250 - 892 — 190 - 392 +16-0 19 100 + 81 + 31 + 867 -4083 +15-0 18 358 — 257 — 227 -15—0 20 448 -447 - 447 -48+0 18 100 - 31 - 31 - 140 -2020 (71H)) BABUB.] PYRO-ELECTRIC PROPERTIES OF ALLOYS. 137 Table 28. — Thermo -electrics of plntinnm alloys — Contiiino,d. No, Ca Nl Co Iron Steel. -48+0 -48+0 1 +49-0 -49+0 -49+0 f-ie+0 -16+0 -16+0 —17+0 < -17+0 -17+0 -18+0 -18+0 I -18+0 f +19-0 +19- +19-0 +20-0 +20-0 +20-0 +-21- +21 +21-0 +40-0 +-40 -0 +40—0 +41-0 +41—0 -41+-0 f— 22+0 -22+0 —22+0 -23+0 -2340 —23+0 -24+0 S -24+0 -24+0 -42+6 —42+0 -42+0 -43+0 -43+0 -43+0 f-50+0 -50+0 -50+0 -51+0 -51+-0 -51+0 23 19 18 23 19 19 18 20 19 18 20 19 18 20 19 19 20 10 19 20 19 19 20 19 20 15 10 20 16 19 15 20 19 13 20 19 15 21 18 20 16 20 21 18 18 23 19 10 24 19 358 448 100 358 448 100 358 448 100 358 448 100 358 448 100 358 448 100 358 448 100 358 448 100 358 448 100 358 448 100 358 448 100 358 448 100 358 448 100 358 448 100 358 448 100 358 448 100 358 448 € obflorveil. e ('.ulcnlatfil. - 320 - 305 - 466 - 466 + 41 + 41 + 173 + 138 + 305 + 305 — 403 -- 403 -1734 -1710 - 2166 —2166 - 745 — 743 -ol90 -3153 -3900 -3990 - 910 — 046 -4134 -4019 -5095 -5095 + 89 + 89 + 61 + 81 - 26 - 26 + 164 + 164 + 253 + 277 + 170 + 170 + 186 ■\- 186 + 149 + 226 + 41 + 41 + :j47 + 347 + 394 + 551 + 327 + 327 + 58 + 58 + 18 + 7 + 01 + 91 - 382 -- 382 -2226 —2200 -3020 -3020 - 402 - 402 —2401 -2392 -:«13 —3313 — 438 -438 -2827 -2818 -30«*J -3962 - 465 — 465 - -2983 -2989 -4274 —4274 - 307 — 307 -1747 - 1730 - 2303 -2393 - 474 - 474 -2945 —2927 4159 --4150 — 368 — 36S 2383 -2419 3483 -3483 10»:. -a+o 10 100 - 302 - 302 -3211 -4334 -2i+0 -10S3 -25+0 SI MS -3230 -3238 -M+D - J77 - J738 -M+0 n 368 -1190 -2253 -M+0 31 148 'Z173 -3123 -17+0 18 - 405 - 40S - seso -W+B -»08 -J64B -17+0 21 4(8 -3583 -3833 - 847 -W7 -3404 -'«+0 SI 358 -1*18 -1833 -**,0 18 4i8 -2B0S -3005 -w+0 IS 100 - 30 - 30 " 287 — 001 — at+o 17 858 - IM - 188 SO US - «1 -201 -M+O 18 100 - IB - 18 - 10 - 771 8n -N+O - 1S« -M+D 20 UD - 100 — IW +a)-o 18 too + 18 + 18 + 378 -1502 -M+O IT 358 -30+0 10 M - 161 - 151 -31+0 18 100 -102 -102 -1841 -Jl+0 368 - 504 -60* Al -31+0 10 448 — T7B -770 -31+0 Itt 100 -ISO — 130 — 1108 — 1CB8 -sa+o -801 -K+0 18 u» -wa -038 —33+0 17 100 - 00 ~ M — tea -1025 -^+0 It 358 - 564 -541 Hn » 448 -758 -768 -3«+0 100 — 153 -2380 18 368 —mi -1581 -M+0 18 448 -2aw -23M8 -35+0 17 MO - 30 - 38 - 378 - 50* -35+0 - soa - 1«l — 3S-I0 10 448 — 203 — 263 -M+O 18 100 -27S -375 — 3170 -1680 Mo —1320 -1387 -se+o 26 448 -I8T3 -1873 -IS+O -110 -*s+o S! 358 — 5S7 -S70 -«6+« 10 448 -- 708 -788 18 100 + 43 + 43 - 60S - 264 +S7-0 » 358 + 308 + 204 +3T— 30 448 + 283 + 268 -48+0 18 50 - 510 -M+0 358 -258 -348 -«+0 a 448 — 338 -338 -a«^n 10 100 -13] - 131 - IMl -3073 sb —3S+0 20 soa -840 -810 -38+0 „." 44n -1166 -1156 BAMUB.] PYROELECTRIC PROPERTIES OF ALLOYS. 139 Tablb 28. — Thermo-electrics of platinum aUof/8 — Continned. No. Bi Zn {—47+0 -47+0 -47+0 +52—0 —52+0 —52+0 +64-0 +54—0 1+54—0 18 22 19 10 94 19 10 24 10 100 358 448 100 868 448 100 358 448 e observed. e calcnlated. 10»XO — 39 — 39 — 443 188 — 184 — 246 — 245 + 18 + 18 + 612 — 248 — 215 — 306 — 396 + 19 + 19 + 296 + 18 + 83 + 24 + 24 io«xfr — 274 - 3288 - 614 Temperature-coefficient — Table 33 contains the final series of data rel- ative to the pyrometric constants of these wires. It contains mean values of the relation a between electrical resistance and temperature for each of the 52 wires of the above table. The marked ends of these, having been wrapped around the little insulating cylinders of porcelain 80 as to form a helix, the platinum spires of which do not touch each other (" open spiral spring"), were exposed to 25°, to lOO^, and to 358o, respectively, in the space of constant temperature of my boiling tubes. To retain the helix, which is never more than 2*° long along its axis, in place, and likewise to connect the terminals of the bridge adjustment with it, the ends of the helix wire are fused to terminals of fairly- thick copper wire. One of these terminals passes through one canal of the porcelain insulator to connect with the upper end of the platinum helix, the other terminal partially through the second canal in a suitable way to connect with the lower end of the helix. The measurements are then made in the customary way. Constancy of temperature along the 2^ of length of helix may be assumed. The total length of platinum wire in the helix is that for which the above data, Table 31, apply. In Table 33 therefore r, is the resistance corresponding to the tem- I>erature T, and a©*"®, «o^ are the mean temperature-coefficients for the intervals of temperature (P to 10(P and Qo to 360°, respectively. Table 33. — Temperature-coefficienU of platinum alloys. No. r rt 10»xa<,'«» 10» X a|po*» f 25 0.760 2.30 2.22 Pt... 100 0.883 . 857 1.296 1 20 0.408 1.78 1.62 1 100 0.464 1 367 0.C30 o 21 0.485 1.46 1.33 An..-" 2 100 0.539 2 357 0.702 3 22 0.542 1. 27 1.00 3 100 0.594 3 1 357 0.744 (793) 140 MEASUREMENT OF HIGH TEMPERATURES. lBirLu54. Table *Xl, — TetHperaiurC'CoefficientH of platimnn aZ/o^«— Contiuoed. No. Ak..< ' 4 23 4 100 4 ' 357 ^1 25 5, 100 r,' WT , 25 6 100 i 6 367 / I Pd..^ Tr Cii.. Ni... Co..-^| 8,' 8 i 19 100 357 19 100 357 9 19 100 9 357 ! 1 10 19 10 100 1 10 or- 1 11 18 11 100 11 357 12 18 12 100 12 357 13 18 13 100 13 357 14 18 14 100 14 357 15 18 15 1(H) 15 357 IG 17 lf> 100 16 357 17 17 17 100 17 357 18 18 IK 100 18 357 19 18 19 100 19 '"l 10»Xao'"» 10»xa,«o»» . . _ 0.413 1.80 1.01 0.468 0.035 0.472 1.46 1.02 0.522 0.075 0.031 1.02 ■ 0.71 0.078 0.794 0.408 1.75 1.62 0.404 0.630 0.441 1.53 1.48 0.494 0.058 0.501 1.29 1.18 0.552 0. 701 0. 40« 1. 72 1.01 0. 4C3 0.628 0. 425 1.03 1.50 0.480 0.041 0.495 1. 28 1.21 0.510 0.097 0.040 0.89 0.83 0.1880 0.821 0.078 0.80 0.72 0. 722 0.847 1.205 0. 20 0.20 1. 225 1.286 0.443 1.68 1.46 0.503 0.668 0.506 1.34 1.19 0.501 0.714 0.073 1.05 0.87 0.730 0.880 0.572 1.09 1.04 0.022 0. 772 (794) BAHU8.J PYRO-ELECTRIC PROPERTIES OF ALLOYS. }V 141 Tajilb 33. — Tempnaturc'rot'jPcicniH of platinuw alloyn—Couiitiued, 20 r rt 0.783 ao"»xHH a,fc,«» X 10" ( 20 0.89 0.74 20 100 0.838 Co... 20 21 357 20 0.986 0.639 1.57 1.30 21 100 0.717 ■ 21 357 0.929 r 22 21 0.708 0.74 0.74 22 100 0.749 22 357 0.8-2 23 21 0. 707 U. tiU 0.04 1 Fc' 23 10;» 0.H38 1 1 23 t><>f 0.»i8 1 1 24 21 1.405 0.37 0.36 24 100 1.446 I 21 357 1.575 f 25 21 0. 5,'{6 1.14 1.00 25 100 0. 583 •j:. 357 0. 726 2 29 100 0.&17 29 357 0.697 30 19 0.848 0.60 o.r»6 30 100 0.805 30 357 1.0.18 f 31 15 0.4^9 0. N'j 1.32 31 100 0. 524 Al..> 31 # 32 357 0.J5S1 0.408 1.56 1.50 ' 32 10«) 0. 400 1 • 32 357 0.014 3,3 17 0.488 l.L'8 i.u! 33 100 0. 539 Mil..' 33 34 357 18 0.680 0.910 0. 52 0.43 34 100 0.980 34 357 0. 001 35 19 0. riii2 2. 13 1.01 3:1 IDi) 1 0. :i.v2 Mo. 3:> 1 \'.t (1. iiiO n. ::7i) 1.76 1.69 30 1(H) 0.4J1 :m» 3,-7 0. 577 ..u:,; UEASDBBMBNT OF HIGH TAfax33.~Ttnii 357 0.D4G M IS 0.301 I.S4 1.14 0.433 1 54 SS7 aM7 (TOO) AABVaJ PyBO-ELECTRIC PROPERTIES OP ALLOYS. 143 PURIFIED WIRES. 1 ^^ 0.223^ A. Thrice i 100 0.273 ^ 2.00 2.65 fused. 357 0.420. 0.200] C. Thrice I 100 0.357 I 2.52 2.58 fiiaed. I 357 0.545. Oeneral digest. — Following, in Table 34, is a general digest of the above results, in which density J^ at zero degrees, specific resistance «<, as obtained from thick (I) and from thin (II) wires at mean room tempera- tares, mean temperature-coefficient a for the large and the small inter- vals (P to 100^ and 0^ to 360°, respectively, specific resistance «© for 0° computed with a, and, finally, the thermo-electric power a \>er degree centigrade at 0<^, are carefully inserted. The data for purified wires are discussed below: Table 34. — Constants of platinum allays. Digest. No. 1 2 3 4 5 8 7 8 10 II 12 13 14 15 48 40 16 17 18 10 20 21 40 41 22 23 24 42 43 50 Metal alloyed to platinam. Platinum . Gold • • « • Uv « • • • « • • • » UO • • • • • SQver ....do ..... . ...do ..... PaUadium . ... do .... . « • • •Ul/ • • a • « Iridium... ....do ..... • • • • ^&w • • • « • Copper . . . ....do ..... ....do ..... ....do ..... . ...do ..... Nickel.... do .. do Cobalt.... ....do ..... ....do ..... ....do ..... ....do ..... Iron ...... do . ...do — do ....do ..... Steel M I (thick) ft II (thin) it 15.55 21.315 15.30 21.288 .18.98 10.13 21.221 22.44 22.68 21.172 25.58 25.23 21.163 19.48 19.78 20.001 22.70 22.96 10.400 34.80 34.61 21.006 10.53 19.67 20.540 21.40 21.54 10.009 23.86 24.50 21.271 10.87 20.11 21.270 21.17 21.07 21. 319 24.43 24.26 20.676 31.51 •32.27 20.600 33.07 34.06 18.803 63.82 63.56 20. 017 25.69 25.98 19.561 65.87 63.78 20.686 21.03 22.44 10.880 27.61 27.54 18.751 33.71 83.38 20.590 30.01 29.17 10.841 40.21 40.29 10.329 34.83 31.72 10.100 44.69 45.24 20.002 24.45 24. C8 20.628 36.80 36.78 20.330 37.57 4L>. 33 19.580 64.62 60.28 19.750 55. 55 62.88 20.886 20.51 29.39 19.581 61.70 60.51 1 10" X a 2.30 1.78 1.45 1.27 1.80 1.46 1.02 1.75 1.53 1.29 1.72 1.63 1.28 0.80 0.80 0.20 1.27 0.20 1.68 L34 1.05 1.00 0.80 1.57 1.30 0.74 0.66 0.37 0.44 1.12 0.44 2.22 1.62 1.33 1.00 1.61 1.02 0.71 1.62 1.48 1.18 L61 1.50 1.21 0.83 0.72 0.20 1.14 0.15 L46 1.10 0.87 1.04 0.74 1.30 0.83 1.27 0.74 0.64 0.36 0.39 0.98 0.39 II (thin) 10»XO 14.91 18.53 540 22.13 1812 24.67 2570 19.06 100 22.28 436 33.97 1301 18.05 - 844 20.00 - 860 23.87 - 1073 19.42 - 2548 20.40 - 3004 23.64 - 5030 31.75 1 - 77 33.59 1021 63.56 867 25.29 - 140 53.60 015 21.67 - 4005 26.84 - 0065 32.76 -11470 28.56 1481 89.62 2560 80.70 3083 44.57 5510 23.07 1038 36.33 - 3887 41.80 - 3060 59.02 - 4085 62.52 - 4222 28,75 - 3240 60.16 - 4500 [/'(0):/(0)jX10» 2.33 1.84 1.40 L33 L87 L70 1.55 1.33 1.76 1.67 1.30 0.01 0.83 0.21 L31 0.34 1.75 1.30 1.11 1.11 0.03 L43 0.74 0.67 0.37 0.40 1.21 0.46 (797) 144 MEASUREMENT OF HIGH TEMPERATUfUBS. {BULL. 51. Table 34. — Constanta of platinum allojf8, JMgeit — ContiDned. No. 51 25 26 27 44 28 29 80 81 32 83 84 35 3G 45 37 40 38 39 47 52 54 53 Metal alloyed to platinum. ...do I Chromium... ...do ... do Tin — do — do Aluminium.. Manganese . . — do Molybdenum — do do Load do Antimony ... Bismuth do Zinc ...do Cadmium A» 19. 952 20.011 20.513 20.157 20.764 21. lOU 20.974 20.449 20.464 20.724 20.807 19.433 21.263 21.261 21. 302 21.180 21. 241 20.753 21. 179 21.329 20. 102 20. 1)75 (2J.3) I (thick) 46.24 28.47 41.75 42.41 32.06 21.78 25.97 39.56 24.68 22.04 26.11 50.11 16.79 19.18 17.61 15.48 17.68 2t).54 16. IH 16.60 47.84 24.75 15.00 II (thin) ft 49.91 27.99 41.39^ 52.90 3L71 22.21 26.27 40.35 25.98 21.88 26.31 49.25 •16.68 19.67 17.17 15.87 17.76 30.14 16.57 44.55 25.17 10«X< 0.77 L14 0.65 0.56 0.95 L55 1.27 0.09 1.56 1.28 0.52 2.13 1.76 2.06 2.28 2.02 1.11 0.64 1.06 0.62 0.49 0.87 1.49^ L20 0.66 1.32 1.50 1.14 0.43 1.94 1.69 1.88 2.23 1.82 1.09 2.10 2.03 0.51 0.32 1.34 1.14 n (IhiD) 49.16 27.37 40.87 62.36 31.09 21.52 25.00 39.80 25.33 21.18 25.64 48.87 15.96 1&95 16.40 14.64 17.00 29.48 15.83 44.19 24.51 losxa - 3306 - 3211 -3738 - 3760 - 3494 - 287 - 10 H- 878 - 1060 - 1398 - 869 - 2800 - 879 - 8170 - 1312 - 503 - 560 - 1201 - 448 + 013 + 290 lf(0):/(0)JXl©» 0.81 1.17 0.06 0.58 0.911 1.S7 1.29 Olio 1.58 1.33 CSS 2.M 1.78 2.13 2.30 2.00 1.12 2.13 0.57 1.41 PURIFIED WIRES A. Thrico fU8Ud. C. Thrico fUH04i. Platinum ......... 12.88 14.02 2.90 2.05 2.52 2.58 12.04 18.27 2.90 . . .do 2.50 DISCUSSION AND INFERENCES. Earlier results. — I fiLall pass rapidly over the above data for density resistance and tbermo-electric behavior, since they are frequently pro- visional. They exhibit a definite method of work carried to an issue. TIio results are of increasing value in proportion as they lead to the relation between electrical resistance and temperature-coefficient of electrical resistance, to which I have already adverted. Ilere I may state that the original attempts to co-ordinate resist- ance and thermoelectric power were made by Dr. Strouhal and myself* in . 383 ; ibid, 1880, vol. U, p. 930. (71)^} BABUB.1 PYBO-ELECTRIC PROPERTIES OP ALLOYS. 145 however, exhibit more complicated relations. Indeed, our data for alloys of silver with platinum, gold, copper, and zinc showed that the results for st^el were due to causes intrinsically different from the causes varying the electrical properties of alloys. Owing partially to this negative result and partially to the necessity of changing our laboratory location from Wttrzburg to Prague and to Washington, these data^ for alloys remained unpublished in Oerman until 1884, and in English* until 1885. In the mean time M. L. Weber ,^ who, at the suggestion of Beetz, had sought for similar relations among the amalgams of mercury, was able to publish a fine and elaborate research on the galvanics and thermo- electrics of those substances. In addition to the results of Strouhal and myself for silver alloys, and Weber's results for amalgams, it was hoped that the present results for platinum alloys would supply such a sufficiency of new data that from all the results thus in hand certain general inferences bearing on the properties of alloys might safely be drawn. This discussion must, however, be deferred for the reasons already mentioned, page 125. Resistance and density. — Turning first to the columns for Jo, «« I, and Sf II, in Table 34, the number of strikingly large values of the specific resistance of platinum alloys at once meets the eye. If the specific re- sistance of good commercial platinum be put «(=13, then it needs but trifling additions of chromium, or iron, or copper, or tin, or manganese, or zinc, etc., to increase this resistance nearly fivefold. In discussing results for silver alloys Dr. Strouhal and I observed that the galvanic effect ])roduced by alloying increased with the diflferences of density of the ingredients of the alloy. In view of the exceptionally high density of platinum and the pronounced tendency of this metal to form alloys of high specific gravity, these inferences seem to be substantiated here, bearing in mind that the differences of density of the ingredients can only be one of many factors which go to determine the properties of the alloy produced. To go into further particulars is undesirable, but I may remark that though the eflfect produced by aluminium is exceptionally small, iridium and gold, both of large densities, produce small increments of resistance, whereas the enormous variations due to tin, chromium, iron, zinc, copper, manganese, cobalt, silver, nickel, palladium, decrease in general in the order of their increasing densities. The absorption of gases', the want of homogeneity, and the very probable tendency to form alloys of definite chemical composition are the main causes which tend to obscure the regularity of the physical phenomena. The diflfer- ences between «, I and «, II, derived, respectively, from the bars and the wires, are no larger than may be easily referred to difficulties of manipu- lation. In the case of chromium, of iron, of cobalt, and of aluminium * Abh. kGiiigl. Bohm. Gesell. Wisa., 6th serios, vol. 12, 1864. « Bull. U. S. Gool. Survey, No. 14, 1885. pp. 76 to 88. 3 Wober : Wied. Ann. vol. 23. 1884, p. 447. (799) Bull, 5i^-^W 146 MEASUREMENT OF HIGH TEMPEBAUURES. [bull. 54. alloys, large discrepancies sometimes occur, sluowing that in these in- stances the base metal can not have been perfectly dissolved nor the alloy satisfactorily homogeneous. Inasmuch, however, as the method of comparing the specific resistance of the ingot as a whole, as it were, with a small part of the wire drawn from it is a very rigorous test for the homogeneity of the alloy, it appears from the coincidence of the results for 8t I and «, II, that melted platinum may indeed be regarded as a solvent for metals generally. The importance of thw quality has already been signalized above. Resistance and ther mo-electrics, — It has been stated that the thermo- electric results are the ones most influenced by impurities in the plati- num, for the alloys of this metal, though exhibiting enormous differences of resistance, are, with few exceptions, relatively without marked thermo- electric variability. This is an observation of importance, particularly if consi(fered with reference to the position of the individual alloys in the series. It shows that there is probably no intrinsic relation what- ever between specific resistance and thermo-electric power when the variations of both the quantities are produced by alloying. Curiously enough the extremes of the thermo-electric variations are the cobalt and the nickel alloys, the former being powerfully positive, the latter even more powerfully negative. The iridium alloy has the well-known ex- treme electro-negative position, as would also have the molybdenum alloys. On the other hand, the i^ositions of iron, of chromium, of man- ganese are not nearly as extreme as would have been anticipated from their resistance values, whereas the powerfully resisting combinations of platinum-copper, platinum-zinc, platinum-tin show only insignificant values of thermo-electric power. In short, there appears to be no law for the co-ordination of the galvanic and thermo electric qualities dis- cernible, and large values in the one case by no means imply large values in the other. Electrical tests for purity. — Having thus briefly discussed the thermo- electric and resistance data in the above tables, it will be next in place to describe the experiments made to ascertain the condition of purity of the platinum used. These experiments have special importance, be- cause they exhibit the electrical behavior of commercial platinum fre- quently treated before the oxyhydrogen blow-pipe, and therefore show what degree of purity of platinum is necessary in order that the metal may be safely used practically in thermo-electric temperature measure, ment. The original experiments made with a length marked A, and cut from the coil above described, behaved in such a way as to give rise to no serious apprehensions. This piece was first annealed, and then thermo-electrically combined with ]N"o. 0, as were the wires in Table 32. (800) BABUB.) PYRO-ELECTRIC PROPERTIES OP ALLOYS. 147 The following data were obtained, nomenclature as above: Tablr 35. — Electrical tests for purity. Number. t T € ob- served. e calca- lated. OX10« 6X10* +il-0... +il--«... +il— 0... 20 18 17 100 358 448 -f 68 + 345 +447 68 335. 446 777 % 554 This wire A was then fused before the oxyhydrogen blow-pipe con- secutively for five minutes each time and tested both for resistance and for thermoelectric ix)wer after each fusion. The results investi- gated range as follows, being obtained, of course, from wires drawn and softened from the buttons, for each case : Tablk 36. — Electrical tests for purity. Treatment GalvanlCR. Tbormo-electrios. n t ^X10« 13.5 Couple. T-t e Before fuHion 913 23 1450 + A-0.... 358—25 +336 After one f oeion . . . 707 23 1890 13.3 +ii-0.... 358—25 +847 After two fusions . . 723 23 1810 13.1 +A-0.... 358 — 25 +337 After three fusions . 710 23 1810 12.9 +A-0.... 358—25 +345 These results give clear evidence of the occurrence of volatilization during the whole of the fifteen minutes of fusion before the blow-pipe. But the amount of variation (6 per cent.), though large in itself, was not relatively so large with reference to the total variation due to alloying (500 per cent.) as to be seriously apprehended. Moreover, the button could be purified by intensely fusing it on lime for some time before alloying it. A second set of experiments, unfortunately made some time after these, gave rise to much more pronounced results. To determine the degree of homogeneity of the wire I compared parts of it of about 100*^°* each, the original positions of which were about equidistant along the whole 130 meters of platinum wire. The gal vanics and thermoelectrics of these samples ranged as follows, each having been softened before testing: Table ^ .^Electrical tests for puHty, Galvanics. 1 No. Tbermo-clectrics. 1 No. Tt t 23 7xl0« 1403 «. t 25 T e B 1115 16.7 — B+0 358 -127 12i0 23 1493 18.2 ~O+0 25 358 -358 D 1198 23 1493 17.9 -2)+0 25 358 -386 E 1185 23 1493 17.7 -j5:+o 25 358 -284 F 1058 23 1403 15.8 + ^-0 25 358 +18 -C^A 25 358 -691 (801) 148 MEASUREMENT OF HIQH TEMPEBATURES. [BULL.M. Ihese wires, -S, 0, D, JS?, jP, were now fhsed thoroaghlj together and kept melted before the blow-pipe for fifteen minutes ; thereupon drawn, annealed, and softened. The new wire on being tested gave the follow- ing results : Tablk ^,—Electrieal ietii for purity. No. Galvanios. No. Thermo^l 504 .23 2781 14.0 25 858 -170 The direct result for e in case of the couple —O+A agrees well with the result which may be compounded from Tables 35 and 37. If now we compare the mean value^i of s, from Table 37 (17.3) and the values in Tables 38 and 39 (15.4, 14.0), it appears that the decrement or volatili- zation of the impurity is greatest during the first minutes of the fusion. Hence, since it was customary to heat the buttons beyond the fusing point for several minutes before alloying, and since, moreover, the range of specific resistances due to alloying is enormously large, it is probable that impurities in the platinum have not distorted the data for resistance and density to a serious extent. The same degree of reliance can not be placed on the thermo-electric data. Indeed, the behavior of the fused sample here is curious. In Table 36, for instance, the values of e oscillate, and are actually greater after the third fusion than originally, whereas the values of «t ^or the same wire, under the same circumstances, decrease with the utmost regularity. The mean values of Table 37, as compared with the values in Tables 38 and 30, show a similar irregularity of decrease. It follows therefore that the results for ax lO^ must be regarded as distorted by an arbitrary constant, which remains nearly the same for a single set of alloys, but which varies from one set to another by an amplitude, the maximum total vajue of which can not be safely put less than 1,000. In other words, the error of ax 10^ from series to series may be as large as ±500. It is only the more powerful thermo-electric combinations in the above, ♦. ^., alloys ot gold, cobalt, silver, manganese, chromium, iroDi (802) K4Eim.l PYBO-ELECTEIC PROPERTIES OF ALLOYS. 149 nickel, indium^ and molybdennm, which fall well outside of this zone of error, and for snch only have thermo-electric inferences been drawn. Mectrioal resistance and its temperature-coeffUiient — 1 have now to touch apon the main results of the present chapter, i. 6., the relation between the resistance (So) and the temperature-coefficient of resistance (a). The results in the digest, Table 34, may be best exhibited in a chart, Fig. 26, in which ax 10^ is represented as a function of «o* It is well to remark in passing that a has been 'calculated by a linear formula, and from the three observations made at ordinary temperatures at 100° and at 357° two values of a may be reasonably deduced, since the measurement at room temperature is less liable to error. The equation a=(r'-r^) / (rtf--rt^) furnishes ao^^ and ao^, both of which are inserted in Table 36. So applies for 0° O. The assumption of the linear form has been wholly a matter of convenience, it being desirable to avoid the excessive computation which would have been necessitated by quadratic forms. The figure contains both a©*^ and ob^, the former of which is given in heavy or large dots; the latter is in comparatively light dots. Vertical lines pass through each datum, and at their ends the name of the plati- num alloy is inscribed. For the sake of comparison, finally, there has been introduced into the chart a curve showing the results which Dr. Strouhal and T formerly obtained for iron-carburets, the data them- selves ranging as follows : Specific electrical resistance and electrical temperature-coefficient of steel. Practical table* $ a 9 a 9 a 9 a cm* cm* cm* cm* mierohm. inicrohm. inicrohm. mierohm. 10 0.0050 21 0. 0033 32 0.0022 , 1 « 0.0017 11 48 22 32 33 21 44 17 12 46 23 31 34 21 45 16 13 44 24 20 36 21 46 16 14 42 25 28 36 20 47 15 15 41 26 27 37 10 48 15 16 39 27 27 38 10 49 , 15 17 3» 28 26 39 19 50 15 18 36 29 25 40 18 60 13 19 35 30 24 41 18 70 13 20 34 31 23 42 17 80 12 This curve is dotted in the figure, the alloy curve being given in a full line. Betuming to the curve for alloys, it appears that the difference be- tween ao^^ and ao^ is not larger than is quite in keeping with the occur- rence of reasonable curvilinear relations between resistance and tem- perature, and that for the present purposes, where a general survey over the whole group of platinum alloys is to be attempted, ao\^ may be accepted as coincident in value with the respective tangents of the » Wied. Ann., voL 20, 1883, p. 525; Bull. U. S. Geol. Survey, No. 14, 1885, p. 19. (803) UEA8UBEMEMT OF lllQH TEMPEKATUBES. (804) BABU8.1 PYRO-ELECTRIC PROPERTIES OF ALLOYS. 151 carviliuear relations in question. Large diflTerences between ao**"^ and ao^ occur in case of one aluminium alloy, two cobalt alloj's, and one silver alloy; bnt the exceptional data of the aluminium alloy, as well as the cobalt alloys, have alresuly been adverted to above in discussing the density and resistance data. In the case of the aluminium alloy, I sus- l>ect that some error of measurement has eluded me, whereas the two cobalt alloys seem to be deficient in homogeneity, as is also the silver alloy. These inferences are permissible, because the remaining alu- minium, cobalt, and silver alloys behave normally, and I am therefore warranted in excluding the three unmistakably exceptional data (Aly Co, Go) from the present considerations altogether. Without any essential restrictions therefore I need only fix attention upon the large black dots of the chart, and from these 52 data it appears clearly that the alloys of platinum may be regarded as a class of mate- rials possessing certain generic physical properties, inasmuch as the effect of alloying platinum with small amounts (less than 10 per cent.) of any other metal is a variation of the limiting ratio of resistance and temperature, when the latter approaches zero, in a way that is inde- pendent of the special ingredients of the alloy from which data may be obtained. Such variation depends only on the resistance-position of this alloy in the class. • In other words, if I put ^t =/(^)? where/ is a series of powers of t then Sq =/(0) and a =f (^)*/(0), and therefore So and a, considered theoret- ically, have to each other relations expressible by a first differential co- efScient. According to the experimental result juststated, furthermore, /(O) :/(0) is such a function of/(0) that the dependence of/(0) :/(0) on /(O) is independent of the ingredients of the alloy by which the varia- tions of /(O) may be produced, provided, of course, the point of view be that of obtaining a broad class distinction for the platinum alloys as a whole, and not to discern rigorously the characteristics of the indi- vidual alloy. To return again to the figure with a view of examining the discrepancies critically, I find that the divergence of data from the mean curve, drawn as carefully as possible through them, is largest to- ward the right-hand half of the figure. This, however, is easily ac- counted for, since in proportion as the resistance of the alloy is greater the results are more and more seriously distorted by an insufficiently homogeneous mixture or by imperfect alloying of the ingredients of the metal. The alloys of nickel, perhaps, are conspicuous as occupying a position above the mean curve, the alloys of copper as falling below it, but for the other alloys a uniformly exceptional position can not be said to be discernible. If the alloying be imperfect the corresponding a will be erroneously large, and a tendency toward over-large values of a is the general character of the discrepancies which the figure presents. Probably, too, the extreme end of the curve already partakes of the divergence, in virtue of which, in a retrograde movement, the diagram positiou of the metal alloyed to platinum must ultimately be reached. (805) 152 MfiAdUREMEKT OF HIGH TEMPEBATURES. [bvluU. Having therefore obtained some general notions of the dependence of f{0):/(0) on/(0), it is next in place to endeavor to inquire into the form of dependence of these two classes of experimental data on each other. With a view of arriving at as simple a relation as possible I have tested the hyperbolic eqnation — (/lO)+i)(/(0):(/(0)+m)=» (I) which contains three constants, and for the computation of which three pairs of values of/(0) and/'(0) :/(0) sufSce. These may be taken from the figure, with some care as regards the judicious selection of points, as follows : /(0)=11.7 f(0) : /(O) 0.00300 20.0 0.00164 60.0 0.00050 If we denote /(O) aud/'(0) :/(0) for a moment by x and y, the values of I and m have the general forms m which, together with equation (1 ) for the special values of x and y, lead to the constants J= -0.1360 m=:0.0002548 n=:0.03764. ' Moreover, the curve (/(0)-0.1360)(/(0):/(0)+0.0002548)=0.03764 ... (4) does not differ appreciably from the curved line which, in Fig. 26, has been accepted as the locus of the larger black dots. Equation (4), however, is exceedingly significant. Inasmuch as/(0) varies between 10 and 70, 1 is generally considerably less than 1 per cent. of/(0). Equation (4) therefore emphatically suggests that a sim- pler form of equation be assumed, in which {=0. Equation (4), how- ever, contains still another striking suggestion. The positive character of the constant m indicates that a larger value than ao'% or the mean temperature-coefficient between zero and 100^, will tend to further simplify equation (4). Now, since, generally, ao^^>ao^, it follows that /(0):/(0)=a>ao'~. Hence, with these modifications implied, /(0)(/(0):/(0)+m)=n (5) will in all probability hold good for the observations as a whole even more nearly than (4). (806) ftAAua.] PYRO-ELECTBIC PB0PEBTIE8 OF' ALLOTS. 153 To avoid complete recaloalation of a it is desirable to investigate some method for passing from a^^ and ao^^ to a. If the values «, ^'j «" correspond to f, f , V\ and if I accept there follows : from which it is easy to deduce g%, 100 ^v **• Now, sV'^9"t^D" and st^—^'^siV are already known from the earlier computations ; and for the present purpose, where a correction only is sought, 9"i? and 9'i? may be neglected as compared with Hif'^ and «^', respectively, t being small in comparison with if and t'^ Hence 100 ^860 a^—a^ which, since tf*%/t'^ is a constant, is a sufficiently convenient form, and much of the correcting may be done mentally. Finally, the three quan- tities ^0^", ar,Qo*^, and a^ have a similarly simple approximate relation to each other ; for -p j^Sq^Xq 7// ^/ = *0^lOO y// _ jT^^^O whence whence, furthermore, for instance, Hf // "0 "0 — j^t ^\ — "100 / and since {f'^f)/(t"'-t) is a constant these reductions are also mental. It has been observed that the corrections throughout affect only a few units of the last Mgure, and it is for this reason that the reductions are simple. As a matter of corroboration a for Nos. 0, 1, 2, 3 was cal- culated directly by the quadratic formula. The results were : No. a=0.002328 1 a=0.001827 2 a=0.001492 3 ty=0.001323 which agree substantially with the other values in Table 34. (8()7) 154 MEASUREMENT OP HIGH TEMPER ATUKEvS. [bvll.U, The values of /(O) and/(0) :/(o) being thus carefully revised it will be expedient to follow the suggestion to whicjh 1 adverted a moment ago, and put /(0)(/'{0):/(0)+m)=^^ (5) By constructing the revised data in Table 31 and taking their graphic mean locus I derive the following pairs of correlative values: i? =12 y =0.00295 X' =25 y' =0.00130 jr"=50 y"=0.00054 from which, deducing the constants m and n, • Wi=0.00022G n=0.0381 and the locus /(0)(/'(0) :/(0)+m)=n does not dillin' appreciably from the mean locus graphically selected. Having thus satisfactorily made this preliminary survey it is finally desirable to calculate the constants m and n by the method of least « squares. Before doing this equation (5) may be i)ut under a better form for practice by writing /'(0):/(0)=-^-»i (6) where yj^ is simply the zero value* of electrical conductivity of the alloy whose temperature-coefficient isf{0) :/(0). Equation (C), when operated on by the method of least squares, does not give inor- dinate pi:eference to the values /(O) of high resistance, and since the high values can not be warranted with a greater degree of accuracy than the low values, equation (0) may most expediently be made the basis of computation. This I have done, and the results in Table 40 contain the observed values of/(0) and/(0) :/(0), the calculated values f(i)) :/(0), and the errors, and finally the constants m and w, with the probable errors J^ (m) and J^ (n) of each, supposing J,(wi)=0.G74 -■i-(-f)" where A- is the number of observations and the factor {1± ') has been suppressed, and where jo and y stand, respectively, for /(O) and f(^) 'fW' The last three alloys, 10, 11, 12, were added subsequently to the calculation. (808) luftm.] PY&O-ELfiCTRIC PROPERTIES OF ALLOYS. 165 Table 40. — Computation of m and n in equation (6). No. fiO) Obwn'iMl. /'(0);/(0)xlO^ 14.91 2.33 1 18.53 l.gl 2 22.13 1.49 3 24.07 i.:« 4 19.06 1.87 7 19.42 1.76 8 20.40 1.67 9 23.64 1.30 13 31.75 0.91 14 33.59 0.83 15 63.56 0.21 48 25.20 1.31 49 bXGO 0.34 16 21.07 1.75 17 26.84 1.39 18* 32.76 1.11 19 2^.56 l.ll 20 39.62 0.93 41 . 23.97 1.43 22 36.33 0.74 23 41.80 0.67 24 59.02 0.37 42 62.52 0.46 43 28.75 1.21 50 60.16 0.46 51 40.16 0.81 25 27.37 1.17 26 40.87 . 0.66 27 62.35 0.58 44 31.09 0.98 28 21.52 1.57 29 25.60 1.29 30 30.86 0.70 32 21.18 1.58 33 25.04 1.33 34 48.87 0.55 35 15.96 2.20 36 18.05 1.78 45 16.40 2.12 37 14.64 2.30 46 17.00 2.09 38 29.48 1.12 47 15.83 2.12 52 44.19 0.57 64 24.51 L41 A 12.04 2.96 C 13. 27 2.50 10 19.42 1.76 11 20.40 1.67 12 23.64 1.30 CalciilaUnl. 2.34 1.84 1.51 1.31 1.79 1.75 1.66 1.40 1.00 o.or. 0.40 1.30 0.51 1.55 1.21 0.96 1.13 0.76 1.38 0.84 0.71 0.44 0.41 1.12 0.43 0.58 1.19 0.73 0.52 1.02 1.56 1.28 0.75 1.59 1.28 O.M 2.18 1.80 2.11 2.38 2.03 1.09 2.19 0.66 1.35 2.04 2.66 1.76 1.66 1.40 Error. xlO» AUoy. 0.01 Pt -6.01 Aa - 0.02 Au — O.OI Au +0.03 Ag +0.01 Pd {0 01 Pd -0. 10 Pd -0.09 Cu - 0.10 Cu 0.19 Cu -i 0. 01 Cu —0.17 Cu + 0.20 Ni +0.18 Ni +0. 15 Ni -0.(2 Co +0.17 Co +0.05 Co -0.10 Fe -0.04 Fe -0.07 Fo +0.05» Fe +0. 09 Fe +0.03 Steel + 0.23 Ste«l —0.02 Cr • -0.07 Cr + 0.06 Cr - 0.04 Cr +0.01 Sn +0.01 Sn - 0.05 Sn - 0.01 Al +0.05 Mn -0.03 Mn + 0.02 Mo —0.02 Mo + 0.01 Mo —0.08 Pb }0.0C Pb +0.03 Sb -0.07 Bi -0.09 Zu +0.06 Zn + 0.02 Pt —0.16 Pt + 0.01 Ir +0.01 Ir —0.10 Ir (809) 156 MEASTIREMKNT OF HIGH TKMPEUATURKS. [buix.64. The constants to which the vaUies of this table refer are m=0.0001939± 0.0000233 n = 0.03778 ± 0.00054 The probable errors of m and n indicate that the inaccuracy is largely incurred in the measurement of /'(()) :/(0), whereas n is much more fully warranted. The equation is one, however, in wiiich pairs of val- ues of m and w, either both larijer or both smaller than the critical values above, readily comjicnsate each other. As usual, the constants which may be derived with a little forethought from careful graphic representations of results are probably nearer the truth than the values which are mechanically computed by the method of least squares. The final results of this chapter may therefore be stated as follows: In endeavoring to describe the platinum alloys as a class possessing generic characteristics, it is permissible to abstract from the minute and individual behavior of the isolated alloy ; and it appears that elec- trical temperatiire-coeflScient /'(O) :/(0) varies as a linear function of conductivity (1 :/(0)) throughout the whole enormous variation of re- sistance (10 to 65 microliuis, c. c.) which i>l{itinum alloys not too highly alloyed (<10 per cent.) pr(^sent. In other words, if at t^ the specific re- sistance of a platinum alloy be denoted by/(/), where ^symbolizes tem- perature, then /(0)(/'(^):/W+0.000194)=0.0378 (7) It is perhaps not superfluous to remark in passing that if instead of the thoroughly arbitrary' temperature 0^ centigrade some other value more in keeping with the qualities of platinum alloys had been selected the constants m and n would present difi'erent values ; and it is easily con- ceivable that correlated values of/(/) and/'(0 may exist, for which the constants is annulled and for which equation (7) takes its simplest form. The actual search for such a result involves more labor than I can at present apply. Clausius ^ was the first to call attention to the approximate proportionality of the resistance of most pure metals with their absolute temperature. Accepting Matthiessen's general relation 8,=8o[l+at-^i^) «=0.00382 y5=0.0000012C and putting it appears that at, say, OO'^^ the said proportionality is accurate. Again, since/(<) increases more rapidly than /'(O decreases, with increasing temperature the passage of the equjitiou /(O) (/'(O) :/{0)+wO=H into/{0/'(0 :/(0)=nS may be looked for in the region of positive f. ^Claiisins: Po^g. Ann., 4th s<»-ri«'s, vol. 11, I'.V, p. (I'O; , ISM, p. ID. *TIio inetaHio iugretlient i>n'sent in tin* alloy in l:ir<4(*r amount is fitly used in dosig- nating the alloy. 3 Matthiessen u. v. Bone: Pogjr. Ann., vol. lir>, ISO'J, p. 3r>:]. < Jeukin, who niado Biniil.ii* hmI net inns in tln^ casci of puro motals by means of lead, arrives at somewhat dirt'orent nnuihors. A satisXiictory absolute table c»U not Ve conotructed, (811) 158 MEASUREMENT OF HIGH TEMPERATURES. f BULL. 54. positions given are volume ];)ercents, except in the case of phosphides and arsenides of copper, where mass percents are meant. Table 40a* — Showing Matthies8en*8 and VogVa results for the electrics of gold, of silver ^ and of copper alloys. Gold Alloys — Alloy. Ao AaCn AnCa AuAg AnAg Composition. A'. 79 56.1 16.1 21.5 15.1 1.6%Cu 18. 3 % Cu 20.1%Ag 47. » % Ag Observed. a X 10« Mi- A«xI0* Silver alloys-..^ Ag •AgCu AgCu AgCa AgPt AgPt AgPt AgPd AgAa 1. 5 % Cu a 2 % Cu 46. 7 % Cu 2. 5 % Pt 5. % Pt 9. 7 % Pt 23. 3 96 Pd 19. 9 % An 109 79.7 80.3 74.9 31.6 18.0 6.7 as 21.7 3.67 2.65 • 0.75 1.11 0.70 3.82 (?)4. 12 2.75 2.80 1.24 0.77 0.33 0.32 0.90 506 359 103 137 9 691 510 514 480 202 115 43 55 139 Calcu« lated. • ■ ax 10* ^axlO^ 3.69 —2 2.63 +2 0.79 —4 1.03 +8 0.74 —4 8.83 ±0 2.88 -13 2.69 + 11 1.20 + 4 0.73 + 4 0.34 - 1 0.41 - 9 0.86 + 4 Copper alloys.. < Cu CuAg CuAg CuAg CnAu CuAu CuFe CuZn CuZn CuZn CoZn CuZn CuSn CuSn CuSn CuSn CuSn CuP CuP CuAh CnAs CuAs 1.6% Ag 4.8%Ag 22.4 % Ag 0.7% Au 19. 2 % Au 5 % Fe 5. % Zn 10.9% Zn 23. 6 % Zn 29. 4 % Zn 42. 1 0.00010 m = - 0. 000112 ± 0. 000031 n = -f- 0. 00538 ±0. 00085 Copper alluys: m = — 0. 000386 -i- 0. 000040 n= -\ 0. 000551 tO. 00012 Gold alloys : Silver alloys ; 102 3.87 653 3.98 —11 89.5 3.45 573 3.54 - 9 82.3 3.25 627 3.29 - 4 69.8 3.03 447 2.85 -fl8 84.0 3.32 638 3.35 - 3 20.5 0.86 131 1.11 -25 38.9 1.55 249 1.76 -21 60.4 2.47 2.52 - 5 46.9 2.05 300 2.04 + 1 21.3 1.88 136 1.14 + 74 21.7 1.27 139 1.15 +12 21.8 1.37 140 1.16 +21 02.5 2.GA 2.59 + 9 19.7 1.00 126 1.08 - 8 12.1 4.69 77 0.89 —12 10.2 0.67 65 0.74 - 7 8.8 0.55 66 0.G9 -14 23.6 1.32 151 1.22 ■fio 7.3 0.48 47 0.64 -16 01.1 2.64 391 2.54 + 10 12.9 0.74 82 0.84 - 10 6.3 0.51 40 0.61 - 9 • Rpjocted. (812) BABUS.I PYRO-ELECTRIC PBOPERTIES OF ALLOYS 159 In interpreting these results grapLically it is necessary to procee(L with cantion; for inasmuch as specific rifeistance enters into them recip- rocally, large values of resistance will be only inadequately representeecific resistances vary enormously. Hence the locus (Fig. 27), if ex- tended for higher percents, must show very decided curvature. More- over, there will be a special locus for each metal alloyed to platinum, which will terminate in the particular co-ordinates /(0),/'(0): /(O) of the metal in question. It is in the neighborhood of the two pairs of /(^)> f'W • /(^)> which (one pair at each end) terminate the locus ex- pressing the general relation between these two quantities, that the curious linear relation iu question seems to hold. In view of the fact that the relation between /(O) and /'(O) : /(O) must ultimately be curvilinear, the inferences to be derived from equa- tion* 6 by making either /(0)=0 or /'(O) : /(0)=:0 are necessarily in- volved. To interpret it, similar relations would first have to be devel- oped for low percentage alloys of many other metals. Nevertheless, these considerations are suggestive. They point to a limit, below which neither the electrical conductivity of metals nor the temperature-co- efficient can be reduced. It appears therefore that a lower limit, both of conductivity and of temperature-coefficient, is among the conditions of metallic conduction, not to say of metallic state. To make what I have here iu mind clearer I will premise the follow- ing: In the case of conduction of electricity in metals (solid or liquid) the effect of temperature is a decided decrease of conductivity, continu- ing so long as temperature increases. In the case of conduction in non-metals or in electrolytes (solid or liquid), on the other hand, the effect of temperature is a decided increase of resistance, which, suppos- ing the liquid state to be retained, continues as temperature increases. Hence conduction in metals is distinguished from conduction in elec- trolytes in this respect, thai if the temperature coeflicient iu one case (metals) be regarded positive its value in the other case (electrolytes) will necessarily be negative. Applying these general principles to the above inferences for alloys, it appears that the occurrence of a lower limit of electrical conductivity and of temperaturecoetiic.ient in the case of alloys may be regarded as significant or as being a unique ex- pression of one of the conditions of metallic condu(;tion. I am thus led to inquire into the nature of tliat class of substances whose temperature-coefficient is zero ; a class of substances, in other words, in which the metallic and the electrolytic modes of electric coa- (817) 164 MEASUREMENT OF HIGH TAMPER ATUBE8. [bull. 64. ductivity may be supposed to converge, for a march from the ex- tremes of high valaes of conductivity possessed by metals or by sab- stances of positive temperature-coefficients to the extremes of low values of conductivity possessed by electrolytes or by substances of negative temperature-coefficients can hardly be supposed possible with the exclusion of the zero temperature-coefficient. The point which I am endeavoring to make becomes even of greater importance if we associate with metallic conductivity the correlative property of optic opacity. Relations between light and electricity have long been investigated, and many curious experimental facts are known. Maxwell's electro-magnetic theory of light furnishes a theoretical basis, for the fact that all true conductors must be exceedingly opaque. Looking for a special application of this general principle it appears that solid metals, no matter how high the temperature to which they are heated, retain positive values for the temperature-coefficient Similarl^p, Govi's^ careful experiments prove beyond a doubt that solid metals, even in extreme 8ta,tes of red heat, remain opatiue. The case of liquid metals is by no means so definitely established; and however uncertain and indefinite the evidence, the questions relative to possible transparency of liquid metals at very high temperatures is an open one.* Considered from an electrical point of view, the increase of resistance of a metal from low temperature to the highest attainable, accompanied, as it ia, by a diminution of the temperature-coefficient, points more em- phatically to an ultimate occurrence of optical transparency after the metal has passed from the solid into the fused state. Finally, inas- much as oi)tical transparency may be considered as having been reached at the critical temperature, it is to this state that the occurrence of the zero temperature-coefficient is to be referred. For the present I may state that the position to be taken with refer- ence to the importance of this paragraph depends solely upon whether or not the result underlying Figs. 26 and 27 is to be taken as the ex- pression of a law. I have ventured to accept it as such. The remainder of the text is an application of s\mi)le geometric methods. I am not conscious of having forced any point, and the equation between /(O) and/'(0) :/(0), at which I finally arrive (l)age 157), follows as an imme- diate inference. If in this equation either the first or second of these quantities be made zero, or if, in other words, the line be prolonged in a negative direction, the predictions of the line a« a whole agree with the known electric behavior of metallic conductors, and with the known electrical behavior of electrolytic conductors, and furthermore suggest the possible occurrence of an intermediate chiss of conductors, such that the passage from metallic to electrolytic conduction may be made con- tinuously. »Govi : C. K., vol. 85, 1«77, p. 099; St'ccbi : Ibid., vol. G4, 1867, p. 778. nV. Ramsay: Chem. News, vol. 55, 1887, pp. 104,175; Turner; Ibid., p. 163^ (818) CHAPTER IV. THEC ALIBRATION OF ELECT^RICAL PYROMETERS BY DIRECT COMPARISON WITH THE AIR THERMOMETER. DISPLACEMENT METHODS OF AIR THERMOMETRY. Some time after the methods for measuring high temperatures and of measaring vapor densities at high temperatures had been fully devel- oped in the admirable manner due to Deville and Troost/ a new method for high temperature vapor densities was published by V. Meyer. A modification was at once introduced by Crafts and Meier, by which V. Meyer's method became available for the measurement of high temper- atures. In these thermometers the gas used, instead of being kept at constant pressure or at constant volume, as in most air thermometers, or instead of being pumped out by a mercury air-pump, as in Deville and Troost's apparatus, is simply chased out by a second gas. If therefore the two gases be collected over a liquid in which the displacing gas only is soluble, the volume of the gas which tills the thermometer at any tem- perature is easily measurable. Air, for instance, may be used for meas- urement, expelled by HCl or CO2, and collected over water. A few minutes suffice for the displacement. Since all operations are conducted under atmospheiic pressure, it is obvious that the Crafts and Meier devices can be used at temperature at which porcelain is seriously vis- cous and permeable to gas. Special forms of the Crafts and Meier apparatus are made by MM. Morlent frferes, among which the tubular form designed by Meyer^ to fit the Fletcher organic combustion furnace would appear to be specially convenient for calibration work. In some earlier experiments Dr. Hal- lock and I endeavored to make use of it. The accompanying diagram, Fig. 28, drawn to the scale ,^„, indicates the method of adjusting the thermometer for calibration. The tubular thermometer of porcelain is shown at AB C, The ends A and C of both of the capillary tubes A F and U Care provided with three-way cocks of special construction, made of brass. Only one of these, D, is shown in the diagram. Fig. 28 being a longitudinal section with an end view cross section through the canals. The thermoelement to be compared with the air thermometer is stretched along its axis with the hot junction at a, the center of figure. The two wires a b and a c pass through the capillary tubes A F and E C and through a corresponding * Cf. Introduction, p. 27 et Heq., where the full references are given. 8V. Meyer: Chem. Ber., vol. 15, !}?*>, p. 1161. (819) 165 166 MEASUREMENT OF HIGH TEMPERATURES. [BULL. 64. SiL «^! Straight capillary canal in the stop-cocks. To prevent escape of air at these holes the wires are, during the measurements, sealed into them with resinous or other cement. The capillary stem of the air thermometer communi- cates, however, with a second capillary canal in the stop- cock Dj a.t right angles with the other canal. It is through this second canal and the three-way cock that either the soluble or the insoluble gas may be introduced into the thermometer, the two lateral tubes d g and ft being in connection with the corresponding gasometers. There is also a hole at n, through which either gasometer may com- municate with the atmosphere. We did not carry this method of calibration into great detail, chiefly because the temperature at any given point of the long tubular space of the Fletcher furnace, as well as the mean temperature of the whole length of tube, proved to be insufficiently constant. Kor can it be as- sumed that the temperature at the center a of Fig. 28 (thermoelement) is identical with the mean temperature of the tubular column of gas. Moreover, since the capacity of the thermometers is not much over 100<^% measure- ments of gas volume must be made with very great care to be in keeping with the accuracy of calibration required. It is also inconvenient to insert a special thermo-element permanently for each series of measurements, the problem of calibration being usually of .such a kind as to make it desirable to compare a series of thermoelements either at once or else in rapid succession. Finally, the thermo- element to be compared must necessarily be filiform and very long, whereas the constants of short thick thermo- elements are frequently in demand. Add to these even more serious sources of error, inasmuch as measurements are made in a tube not glazed internally and with a gas, the rigorous purity of which is not assured. Nevertheless this method of calibration may sometimes be convenient. (Cf. p. 36.) Taking the elaborate gasometric apparatus into account the method is not as simple as it appears. It occurred to me, however, that this simplicity might possibly be reached by displacing dry air with slightly superheated steam. But I made no experiments. The application of Crafts's method, which can easily be made by in- serting a platinum capillary tube into the stem of the air thermometer, deserves special notice, and by the aid of the metallic tubing, to be de- scribed below (Chap. V), can be put to a rigorous test. (820) % . « S i 9 a e o H c ^1 hO BABUM PORCELAIN AIR THERMOMETRY. 167 CONSTANT-VOLUME THERMOMETERS. In most of the present experiments the object has not been to test the rigorous accuracy of the air thermometer so much as to devise forms of apparatus in which such tests can be satisfactorily made. I have had in mmd, moreover, that the thermometer is to be used as a means of calibrating the tbermo-element. Having found therefore that at temperatures not exceeding J,3()0o the porcelain of Bayeux is quite rigid as regards excesses of pressure (intiBrnal or external) not exceed- ing one atmosphere, I made the early airtliermometer measurement^ by the constant- volume method. Jolly's* well-known and convenient ma- nometer was largely used, with such modifications as the special work required. To connect bulb and manometer of the air- thermometer adjust- ment I used capillary metallic tubes. Such tubes had been used by Eegnault^ and otliers l)efore. They enable the observer to place the manometric apparatus at some distance from the furnace and the bulb, a condition of accurate measurement wiiich, at high temperatures, is almost essential. I will briefly describe the apparatus more in detail. The general disposition of apparatus is given in Fig. 20 (frontispieoe), and there will be little dilliculty in recognizing the parts to which the descriptions refer. Further comment is made below (p. 188), Matwmeter, — A very substantial form of manometer stand, made for the work by Mr. William Grunow, of West Point, is shown in the frontis- piece, under B. The stand is essentially that of Jolly, as modified by Professor Pfaundler in Insbruck.^ It consists of two vertical parallel cylindrical slides made of brass, 1(50^'" in length, 2.5*^^™ in diameter, and about 13*''" apart, measuring from center to center. These slides (tubu- lar) are fastened below to a suitably large trii)od support, and are braced above by a slender St. Anthony's cross, the lower end of which abuts against the tripod. Metallic clamps or sleeves, provided with suitable devices for carrying the manometer tubes, are tbus free to slide along the whole vertical range of 100'". A millimeter scale, about two meters long, is placetl between the brass upright for approximate meas- urement. Finer measurenicnts are made with a cathetometer.* Obvi- ously this stand is equally convenient as a support for both the constant volume and the constant pressure apparatus, either of which methods of air thermometry may be used with equal facility. The modification of the Jolly-Pfaundler stand, by which the brace is made to abut against the top of the slides instead of against the mi According to Ronma (cf. Spring: Chem. Ber., toI. 15, 1882, p. 595) silver with a platinmn core (Wollaston's method) is found to alloy after long drawing. I observed no effects of this kind, however, possibly because the metallic surfaces, id case of base metals, are not sufficiently clean. (824) POECELAIN Am THEBMOMETBT. 171 Table 41. — IHmenHanB of copper oapillarg tuba. No. 1 Weight I..e]igth. Thick- ness. Caliber. Vfdnme per om. 9- cm. cm. ctn. ee. 1 5.81 81.5 0.119 0.068 0.0031 2 &39 95.0 0.103 0.050 0.0020 8 10.81 144.0 0.123 0.066 0.0034 4 4.74 e7.8 0. 110 0.064 0.0082 5 7.34 105.6 0.118 0.062 0.0031 6 7.07 108.2 0. 119 1 0.069 0.0037 7 2.90 101.7 0.077 0.041 0.0013 Among these No. 7, a very perfect tube, is most remarkable. The tabes were made in Febmary, 1884. Since that time I was fortanate in inducing the Malvern Platinam Works to undertake the manufacture of such tubing in silver and plati- num. With the latter metal they succeeded well, and the dimensions of samples of the (platinum) tubing made for me are given in Table 42, Table 42. — Dimensions of platinum oapillary tubing. No. Weight Length. 9- em. 1 9.02 51.0 2 7.25 42.6 3 7.07 41. 5 4 7.62 44.4 Thick iiesM. Cttlibor. Volnme per om. 1 ' em. em. ee. 0.115 0.0524 0.00215 0.115 560 246 0.115 561 247 0. 115 1 653 240 These tubes may be obtained in any length not exceeding 5 meters. It is usually sufficient to use meter lengths only, cleaning each thoroughly with naphtha, alkalies, and acids; passing capillary iron wire quite through the tube, drying, and then heating to redness before inserting. The use of capillary tubes presupposes slow rise and fall of temperature during calibration. To this end my furnaces have been constructed. The data of Tables 41 and A2 will appear more striking when placed in contrast with the capacities of tbe bulb and stem of the porcelain gas thermometer. These are 30()'^*^ and 0.012*^*' per centimeter, respectively. Knndt has successfully used capillary glass tubes drawn out so thin as to be filamentary. Platinum capillar^' tubes (the present being the first ever made, I believe) are an especially useful apparatus and subserve many ulterior purposes. They are used, in chap. V, for instance, as an essential part of the transpiration thermometer, and to investigate the laws of transpira- tion and gas viscosity at high temperatures. Porcelain gasthermometer bulbs. — Various forms of gas-thermometer bulbs, as given in Figs. 31, 32, and 33, drawn to a scale of i, were used. (826) 172 MEASUREMENT OP HIGH TEMPERATURES. [bull. 64. They were made by Morlent frferes, Paris* (formerly Mr. Gosse, the original constructor of the Deville and Troost apparatus), of the very refractory porcelain of Bayeux. Fig. 31 is the earliest form. Bulb and Ftg. 31. Non-inglazGd «phencal air tbemiometer bulb. Scale i. Stem are one piece, put together by tlie maker. The fractured bulbs show that the ballon proper, to within a radius of 1"" of the neck {d dj Fig. 4), and the stem with attached neck {b d a d)^ were made separately, and then put together by a skilled artist. After burning no disconti- nuity of porcelain at the circle of junction is visible. The glazed gas- thermometer is perfectly smooth on the outside, and a longitudinal sec- tion differs in no essential respect from Fig. 31. In consequence of the long capillary stem (O.l*™ in diameter) it is exceedingly difficult to glaze these thermometers internally or to keep the stems from choking when the tem])eratures are high enough to soften the glaze. For this reason the bulbs are furnished without being glazed internally — an error when data of high temperature are to be sharply measured. I add here that on fracture the stems very fre- quently reveal clefts and lateral fissures communicating with the canal, I believe that a more compact stem could be made in the manner de- scribed above (p. 95) for the manufacture of porcelain insulators for the thermo-element. M. Gosse pressed his stems in a long mold over a core of zinc wire. The latter is melted and volatilized during the firing ; but in spite of its ingenuity this method is imperfect, for the capillary canals made in this way, in addition to their liability to retain lateral fissures, are seldom perfectly central along the whole length of stem. In case of a stem made by my method this result necessarily follows whenever the apparatus has once been adjusted. In Table 43 some values of the mean dimensions, etc., of the bulbs (Fig. 31) are given,. They are the results of mercury or water calibrations, of which for accurate measurements the water calibrations are prefera- ble. Mercury does not so easily enter the fine fissures. ' I also had similar bulbs made iu Berlin, and will commnnlcate results obtained them later. (826) 1IABU8.] PORCELAIN AIK THERMOMETKY. 173 Tablk 43. — Capacity f etc., of porcelain tfas'thermomeier bulb$. No. Bull). Moau Stein. I Equatorial tul^t"" , Cnmieitv L.uffth '^^^^^' ^^^ Volume cliameter. V,!* ij" i**" ^«P«»*^">- , ^<^^R^^' new*. I c«Uber. per cm. •> 3 CM. 9 9 nn. 0.27 o.::o ee. :ti)0. :{07. 4 cm. 40 40 em. 0.8 0.8 cin. 0.122 ee. 0. 0116 Probably owing to difiicultios in burniug the polar diameter is usually sbghtly less than the equatorial diameter. To use this bulb for calibration it is necessary to have a space of very constant temperature, for the indications of the thermoelement are in- stantaneous, and refer only to the little space immediately surrounding the thetmo-electric junction, whereas the gas thermometer passes rela- tively slowly from one temperature to another, and the temperature datum refers to the internal mean temperature of the whole exposed surface. These ditterences of character in the respective temperature in- dications may, of course, be seriously large. They are entirely arbitrary. With the object of eliminating these errors I had a bulb made in the shape of Fig. 32, the bottom of which is re-entrant, forming a cylindri- ^fOC^TtA ^^^^^^^^^^<^^^^^ ^^ ^^^^i^>:^^i:i^illilll^^^ Fig. 32. Non-injKlazed re-cntmnt air tbermomet4»r bulb. Scale \. cal tube, n wi, the closed end m of which i)roject8 inward as far as the center of the bulb. It is into this tube that the properly insulated thermoelement is introduced with its junction at wi. The insulators are suflBciently large to practically close the tube n m as with a plug, by which loss of heat by radiation is made iuii)erceptible. The tempera- ture of the thermoelement and of the gas thermometer may therefore be regarded identical. I add that the stem of the form (Fig. 32) is thicker than the stem in Fig. 31, in order that at high temperatures there may be less liability to bending, su})posing the thermometer to be held in a horizontal position and the stem to be slightly viscous. The widening (827) J 174 MEASUREMENT OF HIGH TEMPERATURES. (bullM. of the stem does not seriously increase the value of the stem error by. increasing the number of interstitial pores, as will be seen. In this re-eutrant bulb symmetry of form has been sacrificed in order that greater identity in the exposure of the air thermometer and of the thermocouple may be secured. Deville and Troost emphasize the desirability of spherical bulbs. But the expansion error is beyond question less serious than the calibration en or, due to inequalities of temperature of bulb and thermo-electric junction . The pressure which bulbs of this kind can withstand at high red heat (1,0000) without deforming appreciably is certainly greater than an atmosphere, probably much more. Bulbs in which water is confined explode at high temperature with detonation and great violence. The results obtained with these forms of internally unglazed gas thermometers are called in question by Deville and Troost. Doubtless gas or moisture is forcibly retained in the pores of the porcelain. Hence the amount of gas in the bulb at low temperatures may be greater than the pressure datum indicates. Again, in the constant-pressure method of measurement the volume of the bulb, an essential part of the argument of the formula, can not be sharply defined. Hence the great desirability of performing the measurements with bulbs of porcelain, glazed thoroughly both within and without. Such a form is given in Fig. 33. Fio. 33. Inglazed spherical air thennomoter balb. Scale ^. Bulb cdk and stem e b are here distinct parts. They are calibrated separately, and prior to using are soldered together with feldspar and the oxyhydrogen blowpipe. The bulb cdJc ends in a short neck, cdrs^ the part rc9 being jast large enough to receive the stem e/ snugly. The canal c d, through which the bulb is glazed, eventually becomes the prolongation of the capillary canal of the stem. Soldering together the bulb and stem is a difficult operation, and calls for much skill and patience on the part of the operator. The bulbs are liable to breakage, and it is difficult so to solder the stem that the joint may be hermetically sealed. I therefore feel justified in describing a machine of my own, by which such soldering can be effected. (828) POBCEI.AIN A.IE THEBMOMETBY. 175 Machine for aoldermg porcelain — The elevation (Fig. 34) is largely in section, the cats being taken throngh central planes of the apparatas, as will readily be nuderstood by consaltiDg the plan (Fig.35), I give the drawing in a scale of ■^. The soldering machine cx)UBiBtA essentially of a whirling-table, of which A li iA the large pulley and C D the spindle. The two wheels are connected by ronud leather belting, which can be tightened at pleasure by a aciew atljustmeut, E F, The spindle axle (839) 176 tIEASUBEMENT OF HIOU TEUPEBATUBK8. [bull.h. carriee tbe gas thermometer bulb ^ i? to be soldered to the stem L K. The two pEu^llel plates of brass, ^Jlf, JfS, held at any desirable dis- tance apart by three bolts, b a, subserve the purpose of secnriog the bnib G^ilnnly and symmetrically ith respect to the axis of rotation. It is easily seen that the two plates itf M and y S" make with the balb G Ha joint mat is practically of ,th« ball-and-socket kind, hence the facility of adjustment A lateral arm, P, clamped to the fixed up- right rod Q B, holds the stem K L iu positiou during the rotation, tbe latter passing through a little ring at P. Another lateral arm, U T, similarly clamped to the rod Q R curries the adjustable lime furnace. This is a rectangular parallelopi- petlon sawed outof asolid piece of liiue, provided with a large central (lorforation passing quite through the block for the reception of the neck and lower stem of the gas- thermometer; provided also with a smaller lateral perforation passing only far enough to cooiinunicate with the central hole. This block of lime is secured between two par- allel plates of iron by aid of three bolts, two of which only appear in the figure. Tbe plates are, of course, ring-shaped, to correspond with tbe vertical perforation of the lime block, and the lower plate is rireted to the lateral arm U T. To obviate confusion of lines the lime furnace is omitted in the plan (Fig. 3D}. I ueed only add that the arms P and U T can be removed at pleasure; that the bulb, with its lantern-like support, cau be with- drawn from the spindle by nn- clamping the screw TFj that, finally, the spindle itself is adjustable laterally at pleasure, passing, as it does, between two aliden, A'Xand T Y, These slides are kept in position by two pairs of screws, by which, moreover, the slides and the base plate of the spindle may be foiced firmly in contact and clamped. BAEUB.] PORCELAIN AIB THERMOMETRY. 177 Having given the arrangement of the rotational apparatus, I have to add a description of the sliding oxyhydrogen blow-pipe. The blow- pipe itself is shown at cd^ and the plan contains dotted lines showing the construction of the interior. Hydrogen from the gasometers enters through a large tubulure, o, fully 0.5*"" in diameter, compressed oxygen through a finer tubulure, dj the jet end of which is not quite 0.08"^ in diameter. This blow-pipe burns quietly, and if well constructed the flame is visibly one foot in length, tapering with perfect regularity from the large diameter 0.5''"* to a point. The attachment of this blow- pipe to the frame- work which carries it is such that in its horizontal position the flame plays through the lateral hole of the lime furnace, impinging upon the neck of the bulb to be soldered. The collar n, into which the blow-pipe is fastened by the screw e, has a lateral axis or swivel, in virtue of which the blow-pipe may be rotated around an axis perpendicular to itself (a kind of trunnion), and clamped at any given angle by the screw Jc. In this way the flame may be made to impinge against any part of the stem or neck of the bulb to be soldered, at pleasure. The sliding arrangement into which the swivel is clamped consists of two parts, the slide proper, 5, moving freely along the rod efy and the part w, which is practically a nut of the male screw g h. The parts q and m can be joined at pleasure by aid of the steel pin s 8 and corresi)onding clamp screw. If the latter be loosened the blow-pipe may be made to approach the air thermometer as near as desirable. The screw ^ A ends in a wheel, it, rotated by a belt, which passes over the lower spindle of the pulley-wheel A B. An axle, Ic kj carries two inde- pendent rollers, by which the direction of the belt is changed. In this way the screw is kept in motion to correspond with the rotation of the air-thermometer bulb. When the flame is lit and the soldering commenced, the blow-pipe car- riage is placed as near as practicable to the end h of the screw. As the rotation continues the flame gradually approaches the air thermometer, and the heat is therefore intensified with perfect regularity. Inasmuch as the flame impinges on the neck while in a state of rotation, it is quite obvious that the liability to fracture or breakage is by this device di- minished to a minimum. I add that to prevent interferences the thread at the end of the screw g h has been cut away, so that when the nut m is near these end points there may be no further tendency to move. An intermediate rod, r r, and a sliding piece, e f, increases the steadiness of motion. The carriage as a whole is supx)orted by two up- rights, J J and Z Z. The feldspar to be used for soldering is to be ground most carefully to an impalpable powder and mixed with mucilage or water to a plastic or pasty consistency. This is spread uniformly around the neck of the bulb, so as to form a ring where the edge of the neck shoulders against the stem. It is then allowed to dry. Stem and neck should fit snugly from the outset ; at least all waste space should be calked with feldspar, Bull, 54 — «12 (831) 178 MEASUREMENT OF HIGH TEMPERATURES. [bull. 54. It is perhaps best to commence the heating with the lime faruace re- moved, sliding it above the neck. When the parts are white hot and the frothing has largely ceased, it is expedient to conduct the farther soldering by hand directly, the blow-pipe being for this purpose manipulated by the right hand and the spindle turned suitably with the left. Care must be taken not to melt the porcelain. The heat is, however, siifl&cient to make porcelain quite viscous, and not only can the stem be bent, but the parts of the neck of the bulb surrounding the lower end of the stem may be pressed firmly against it, producing a weld joint, as it were. I have no doubt that porcelain can actually be welded in this way. Flat steel pliers, which if necessary may be notched by a cylindrical hole which tits closely around the neck, are closed quietly but firmly around the neck and then quickly withdrawn, rota- tion of the bulb being temporarily discontinued. The operation calls for skilled manipulation. Indeed, it is not easy to make a vacuum- proof joint, and samples neat in external appearance have frequently to be duplicated. It is essential to keep the whole neck at white heat a long time in order that its inner surface and the outer surface of the stem may be everywhere in contact. It'is at this stage of the operation that the lime furnace may be appropriately lowered, and the final gradual coalescence of contiguous parts of the porcelain apparatus allowed to take pla<5e. Two oxyhydrogen flames impinging on the por- celain from opposite directions are preferable to a single flame with the lime furnace. The latter is essential, however, during cooling. Por- celain is specially liable to crack on cooling when it first becomes rigid. Hence it is expedient, after withdrawing the flame, to close up the fur- nace as far as possible with asbestus board and carded asbestus, and then to bury the whole furnace above the plate mmino, heap of slacked lime. But with the best precautions the feldspar is found to be fissured after cooling, and unless bulb and stem have thoroughly coalesced and the joint be perfect at the internal faces, the apparatus will not be vacuum-proof. It is well to fuse feldspar upon the end of the stem around the hole. To keep this hole opposite the capillary hole in the neck a thick platinum tube or wire may be thrust through both. In this case the neck of the bulb may be quite filled with the slimy feld- spar paste, and the stem then forced into it from above, keeping the capillary platinum tube in place. The feldspar which exudes is par- tially removed, and the bulb then allowed to dry. This process gives greater assurance that soldering will take place between the inner sur- face of the neck and the end of the stem than any other. I may add, in closing, that I have repeatedly tried to make air thermometers in which a capillary platinum tube is soldered into the stem with a glaze more fusible than feldspar. I have also attempted to glaze single- piece air thermometers, like Fig. 31, internally, as well as to solder platitiuiu tubes into the stem. Although these attemx>ts have thus far failed, it is but just to assert that the failures are due rather to the insufficient (832) BABUB.] PORCELAIN AIR THERMOMETRT. 179 technical skill of the operator than to crucial errors of method. I hope at an early day to produce a porcelain air thermometer made in one piece, glazed within and without, and provided with a tight-fitting cap- illary platinum stem. I also hope to make bulbs of fireclay, suitably glazed without, apparatus which will be available for the measurement of temperature very much beyond the highest limit of the porcelain thermometer. The soldered air thermometer presupposes low-pressure measurements, such as this paper describes. Bulbs which are not perfectly tight may sometimes be closed by heat- ing in a large furnace with glaze. I have used the one described below for this purpose. This process, however, is difficult and expensive, even if low pressure is applied to suck the glaze into the capillary fissures and canals. It is best to endeavor to complete the soldering with the oxy- hydrogen flame, testing the quality of the joint with the air-pump after the bulb is again cold. It is well to insert a word here about gasometers. I used the simple form of sheet zinc bell-jar (Fig. 35a), dipping in a reservoir of /n/. TtVi Fio. 35a. Gasometers. Scale ^. water, II mm. The bell -jar is provided with a guide, n n, and a coun- terpoise, K. The level of the water is shown at 1 1, Gasometers of this kfnd are well known, and are furnished by Ritchie & Co., in Boston. My purpose in this place is to indicate the great advantage gained by two stop-cocks, Bj C, for each jar, 0,0 O; for in this way any number of single jars may be coupled together. In Fig. 35a, for instance, the (833) 180 BfEASUBEMENT OF HIGH TEMPERATURES. [bull. 64. Stop-cock B is supposed to be in commanication with the hydrogen generator; the stop-cocks and 1) are connected by rubber tubing; tbe stopcock JE, finally, sux>plies the hydrogen to the blow-pipe, with which it is in communication. The advantage gained in this way is this, that the hydrogen may be generated and used at the same time — a desideratqm when large quantities of the gas are necessary. Revolving muffle. — In order that the temperature comparisons in ques- tion may be satisfactorily made, the apparatus to be compared must be placed in a space of practically constant temperature, which shall be variable at pleasure from ordinary temperatures to the most extreme degrees of white heat. Methods for securing constant temperatures for thermoelectric comparisons have already been given; but when one of the pieces of apparatus to be heated is as large as the bulb of an air thermometer, and when, moreover, this relatively large apparatus is to be compared with the sensitive point of the thermo-element, the diffi- culties of calibration are very much increased. In some of the earlier comparisons the efficient assay muffle-furnace made by the Buflfalo Dental Manufacturing Company was used. This is l>ractically a gi- gantic Bunsen burner, surmounteil by a furnace of tire-clay, so con- structed that the fiame in a narrow sheet is compelled to pass around and completely to envelop the muffle. In the furnace used this muffle was fully 20'^'" long and 12^'" high, ofteiing ample space for the introduc- tion of the bulb, and by wrapping asbestus paper and carded asbestus thickly around the bulb so as quite to fill the muffle, and binding muffle and thermo-element closely together, the two may be compared with some accuracy, Eesults of this kind are given below (p. 201.) Unfortunately the introduction of metal envelopes is objectionable, in view of the danger of fluxing the contiguous parts of refractory clay. There are other and more serious difficulties encountered. The maximum tem|)erature thus attainable is not greater than l,000o, and hence the in- terval of calibration is limited. Moreover, the closed end of the muffle is at the center of heat of the furnace, whereas the open end is neither surrounded by flame nor are the provisions against loss of heat suffi- cient for constant temperature — conditions which recommend the fur- nace for assay purposes, but which, inasmuch as they involve difter- ences of temperature of several hundred degrees, are seriously objec- tionable for calibration purposes. Again, the rate of cooling of this furnace is too great. It is difficult to close up so completely as to exclude convective cooling due to currents of air and diminish loss by radiation, the bottom of the furnace over the burner being large, open, and inaccessible, and the chimney large. Xor is it conveniently ])ossible to regulate the flame of the burner for intensities of heat less than the maximum. Finally, thermo elements must be compared singly, because they need to be tied to the bulb. In general consecutive com- parisons of series of elements are desired. Without question the form of the furnace could be modified to meet (834) tlAtttTB-l PORCELAIN AIR THERMOMETRY. 181 the special requirements of the calibration problem, excepting, of coarse; the limited scope of temperature; bnt it is expedient to proceed more radically and introduce an entirely new and distinct furnace for the pur. X>ose8 in question. This I have done in a way indicated in plan in the diagrammatic Fig. 3G. The body of the furnace is a thick cylin- drical box, B By surmounted by a hemispherical lid suitably perforated. In this cylindrical inclosuie a sphericiil muffle, provided with hollow lateral arms or axles, E and Fy and placed symmetrically with respect to the center of figure of the furnace, is free to rotate around the hori- zontal axis of the arms. If the rate of rotation be sufficient this mech- anism insures constancy of temperature within the mnffle around the horizontal JBF. Two blast burners, and H, purposely placed tangen- ^toUy or dictgonallyy so as to be equivalent to a couple, blow a cyclone of flame into this furnace, equalizing temperature around the central vertical. Virtually therefore the muffle, regarded as a geometrical Pin. 3(k». BllipUo revolving maffle ; diafi^ram. Fia. 36. Rovolving maffle ; diagram. sphere, has two rotations, one about an axis, J57 -F, a second around the vertical, passing through 0. To make this apparatus theoretically per- fect a third rotation around an axis passing through and perpendic- ular toEF would have to be supplied. This third rotation is a mechan- ical impossibility, bearing always in mind that cumbersome or compli- cated apparatus would rather detract from the end to be attained than add to it The two rotations can be made to suffice. In Ihe spherical space of constant temperature thus o>)tained is placed the bulb of the air thermometer, with its stem projecting into and through the arm F* The center of bulb and tlmtot' nuiilie a . nearly as possible coincide. The bulb is held in i)osition and free from the muffle by a clamp attached to stem on the outside of the fur v ace. The thermoelement is intro- duced through the opposite arm E in such a way that the junction may be contiguous with the air thermometer. The insulating tubulure is also supported by a clamp on the outside of the furnace. It is an essen- tial part of the construction of the present apparatus that during rota- tion the muffle touches neither the air thermometer nor the thermo- element, both of which apparatus are stationary, and suspended quite free from all parts of the furnace. Having thus indicated the general principles of the constant temper- ature apparatus, I shall next describe the practical form of this fur- naoe, which, after many trials, has been found satisfactorily serviceable, (835) '182 MEASUREMENT OP HIGH TfiMPERATlTRES. iBULL.6i. This is given in front elevation and longitudiqal section in Fig. 37 and in side elevation in Fig. 38, respectively, drawn one-fourth and onebalf the actual size. The body of the furnace is shown at B B B BjSh thick- walled cylindrical pot, surmounted by a hemispherical dome, A A Aj the Hd of the furnace. A central hole at A' and a series of six sym- metric lateral holes, aa^ aa^ . . .in the lid are sufficient for the escape of the products of combustion. The burners HE HE and O GO G project into the furnace as far as the inner surface. Their diagonal position is well shown in the side elevation (Fig. 38) and their internal construction in the longitudinal section of Fig. 37. Compressed air from a centrifugal blower, run by a one horse- power gas engine, enters the central tubes h h and gg, respect- ively. The inlets of gas are shown at c and &. Attached to the bot- tom of the burners are rectangular slides II and KK^ respectively, which pass through guides L L and MM, In this way the burners can be easily inserted or withdrawn from the furnace. A little pin, d, prevents their being inserted too far into the interior, and a similar longer pin or roller, c, is so adjusted as to rest the gre^t^er part or the whole of their weight upon the bed plate 8 /S, instead of on the friable mass of the furnace. The burners shown in the figure were constructed entirely of gas pipe, and the disposition of parts is such as suggested itself after many trials. Burners in which back explosion is obviated by surrounding the mouths with a sieve or net-work of iron wire (as is the case in some of Fletcher's apparatus) are thoroughly unsatisfactory. These sieves obstruct the blast and are not as much a safeguard against back explosions as is necessary in an apparatus where constancy, or at least very uniform variation of temperature, is the requisite. In the blower of Fig. 37 the blast tube h h extends to within an inch of the mouth of the burner. The column of gas surrounds this tube. With the fol^ current of air sent through the furnace the gas may therefore be as nearly cut off as is at all desirable, or it may be quite cut off without incurring any risk of explosion, either in the blower or in the burner. I may add that the tubes c c and & d for gas supply should both point toward the more accessible side of the furnace, and there communicate with graduated stop-cocks, such as are furnished by the Buffalo Dental Company. For the furnace above half-inch supply-cocks are sufficient. The centrifugal blower which I used was of rather a smaller form than is usual in the market, being only about eleven inches in diameter and with paddles scarcely two and a Jialf inches wide. It was taken from a port- able forge. Doubtless even a smaller blower, i. e., a narrower blower, would have been desirable, so that the power of the engine may be spent in furnishing pressure of blast rather than quantity of air. The smallest form of Root blower (blacksmith's model) and larger forms of centrifugal blower had therefore to be discanled, for with the available power the blast obtained proved to be too large in quantity and too small in intendity. In the Boot blower, moreover, the flame obtained (836) ^^S&SL. '1 *, r i i ^ i I 1 i t . r- i I • » ■ 4* y ■ ,> / ••• * 7 BARU8.J PORCELAIN AIR THERMOMETRY. 183 is intermittent, and in this respect objectionable. It will be well to state that the fiame issuing at the mouth of the burner when the blast is cut off (a great torch fully two feet in length) is reducQcl to a blue cone scarcely eight inches in length for the maximum supply of gas. Placed in the position given the burners during the heating do not melt, but merely grow red hot at the mouth, and the oxidation is a minimum, because the general tendency is to reduce. It is v«^ell, however, to attach a reservoir of water behind the furnace and to tap it through lead piping and small faucets, so as to fall drop by drop upon the burners and thus prevent all possibility of superheating. In none of ray experiments did ferruginous fluxing of the furnace body occur. I found in the experiments that to secure the maximum tem- perature desirable (say 1,400^), it was not necessary to open the half- inch clear- way cocks more than one-third. From this downward the intensity may be diminished to the merest ribbon of flame, sending in reality only a vortex of hot air through the furnace. Indeed this ad- justment is very satisfactory, so that with an accurately graduated arc attached to the cocks it is possible, after the necessary preliminary measurements have been made, to open it in such a way as to strike any given temperature with some nicety. The cupola A A, which can be lifted off from the body B B, along the plane A Aj emphasized in Fig. 38, has a suitable handle arrangement attached to it, which is omitted in the figure. Having thus given a furnace which can be heated to any reasonable degree of temperature with extreme ease and convenience, I proceed next with the description of the revolving muffle. The muffle proper is shown at E D F/in Fig. 37, and consists of two identical halves of refractory fire-clay, each of which is a hemisphere with two dia- metrically opposite guttered arms. The two halves are placed together, with their plane faces contiguous, but without cement. They are held together by surrounding their ends with appropriate collars of iron, N N ^ iV'and N' N' N' N^^ the outer edges of which are widely flanged. These flanges, P P and P P', are turned circularly, with their circum- ferences carefully beveled, so as to fit nicely into the grooves of two pairs of friction-rollers, Q Q and (^ (y, of which B R and iJ' iZ' are the respective axes. Here I may well say that it is difficult to bake the muffle in such a way that the plane faces are not warped. More- over, the two tubes, when placed together, show rather an elliptic ring- shai)ed section than a circular one, as is represented, with a little ex- aggeration perhaps, at //, Fig. 38. But this irregularity furnishes an exceedingly satisfactory way of fastening the muffle into the collar. For if the width of the bore be so chosen as to fit snugly on the major diameter of the axle of the muffle, a flattOvj-shaped spring of steel may be inserted in each narrow space between axle and collar, against the bulge of which (spring) set-screws tttt^ sunk into an equatorial rib of the collar, press as firmly as is permissible ; or this space may be (837) 184 MEASUREMENT OP HIGH TEMPERATURES. [buli.54. filled with fitting knife edged blades of steel, or with asbestns board, against which the screws t press. All of these methods are good. Even when the temperature is so high as to fuse the inner surface of the collar the screws t can be worked loose with a drop of oil or petro- leum, and after removal show no serious injury. It is not easy to fit the axle of the muffle iato the iron collar, because the silicious material does not yield easily to the file. It may, however, be ground on a grind- stone, or, with greater advantage, by filing it with a piece of its own substance. Having thus shown how to fasten the collars symmetrically, and at such a distance apart that the opposed flanges may fit in the grooves of the opposed rollers Q, Q and ^, ^, it is next in order to describe the adjustment of the rollers themselves. Their axles, £, 12, R\ £', are mounted at suitable distances apart on a rectangular rod of cast-iron, u u, provided with a handle of wood, W. The rods u tt, u^ vf again are each a^ustably fastened to Y shaped uprights F, F, F, Y^ and P, F, r, Y' by aid of strong screws F, P. Loosening Y or Y' the rod uuox u' u' may be raised or lowered or rotated around the center of F or y and clamped in any desired position. It is in this way that the inner edge of the collars N NN Nj N' N* N' N' may be nicely adjusted with reference to the lateral shouldered holes of the furnace through which the axle of the muffle projects. Botation therefore takes place on the friction-rollers, in which the wheel or flange P P rolls smoothly. It will be seen that some such arrangement as this is essential, for the rolling parts must be placed so far away from the hot parts that they may be lubricated. At very high temperatures the muffle becomes more or less viscous, and hence it is necessary to obviate all such ten- dencies to twist or wrench off the axles as an imperfectly oiled mechan- ism constantly presents. There is one further adjustment to be made : After the firing neither do the axles of the muffles coincide in prolonga- tion, nor are the axes of the cylinders straight lines. Hence the axles of the rollers R JK, R* K are long cylindrical rods along which the rollers QQ Q Q may slide laterally, their extreme positions being fixed by four adjustable set-screw collars j?, o?, x', a/. To revolve the muffle a belt pulley of wood Z Z has been screwed to the flange- wheel P at a little distance from it. Over this passes round- leather belting, and the power is communicated by a corresponding pulley on a lateral shaft of the engine. The wooden belt-ring Z Z is far enough away from the hot parts to escape being charred. The belt, however, must be provided with a tightener. » »The uprights were given the Y-Hhaped form to prevent the possibility of lateral slipping of the muffle. In later experiments I fonud this safeguard uunecessary, no that a simple flat upright, with a vertical slot opening upward to admit the sctowm r, P, is far preferable. In other words, the uprights in the figure are to be sawed off square above the slot. By this means greater facility of adjustment is secnred when the collar is to be titted to the axle of the muffle or removed from it. (838) L If 4 I . I IC ^t BABU8.J PORCELAIN AIR THERMOMETRY. 185 Finally, the figure shows the air thermometer// k % ein position, sup- ported by the universal clamp m m attached to the vertical rod qq, A similar universal clamp, n n, on the opposite side of the furnace supports the insulator of the ther mo-element A; k. The clamp n n attached to the rod r should be a spring, so that elements may easily be either inserted or withdrawn. The ends of the wires of the thermo-couple appear at a and /5 and pass thence to a petroleum bath 'of known temperature, where they are suitably connected (page — ) with the terminals of the measuring apparatus. The junction of the thermo-element is in contact either with the external surface or with the closed end of the re-entrant tube, according to the form of porcelain bulb selected. - Of this further mention will be made. It is here in place to state the method of insert- ing the air thermometer, a method which must be convenient and expe- ditious. Supposing the collars i\r . . . , JV' . . . to be removed theairther* mometer bulb is covered properly by the two halves of the muffle. The collars themselves are completely cut through on one side by a slit be- tween two nearly contiguous axial planes, which slit passes through the flange P P, as shown at « n in Fig. 3d, as well as through the body of the collar, and is quite large enough to admit the capillary platinum tube of the air-thermometer. This slit does not seriously weaken the collar, strengthened as it is by the central rib into which the screws t are sunk, and by the flange P P. In this way the collar at the air-thermometer end of the muffle may be slipped on quite as readily as the other. Hav- ing therefore centered .the muffle, as described above, it is then easy to fix and center the air thermometer, so that it may be quite free from contact with the muffle. In the case where a soldered air-thermometer of the form Fig. 33 is used, a muffle of an axis sufficiently wide to accom- modate the neck must be used. A muffle of this kind is given in sec- tion in the diagram. Fig. 36. In place of adjusting the muffle it is often desirable to adjust the furnace. This may be done by four set-screws, tttty Fig. 38, which act in pairs at right angles to each other. An oil- dropper, by which the roller Q may be kept lubricated, is a- desirable addition. Some such non essential parts are omitted in the figure to prevent confusion of lines. Remarks regarding the apparatus and manipulation. — Bearing in mind that this furnace is as nearly as is practically convenient or possible the outcome of a theoretical principle for the construction of constant- temperature apparatus, that all manipulations to be applied may be made safely and with expedition, it is well to summarize the advantage gained, as well as to allude to such others as are easily within reach. The maximum temperature obtainable is indefinitely high, much higher than can be define-(<-$^'-'!-:fD]=^ (" where F, F', F" . . . are zero volumes whose special temperatures are T, T', T" , . , for the pressure J7, and f, <', i" ... for the pressure /*, where A is proportional to the excess of volume at T over that of the fixed mass of gas at t, and where a is the coefficient of expansion of the (842) HABus.] PORCELAIN AIR TIIERMOMETRY. 189 gas and /? the coefficient of cubical expansion of bulb, stem, etc. The eqaation asbumes that the gas is i)erfect and that the bulb expands pro- ]K>rtioually to its temperature. The equation is sufficient for the calcu- lation of any one of the variables involved, supposing all the others to be known. In the method of constant volume, A=0. In high-temperature measurement there are at least three parts of the air thermometer to be considered. The first of these is the hot re- gion, and includes the bulb and the part of the stem at the same tem- perature; the second is the part of the stem in which temi>erature varies from the high value to that of the atmosphere; the third is the part in which the temperature is practically that of the atmosphere, and it in- cludes the cold part of the porcelain stem, the capillary tubes, and the space of cold air above the meniscus of mercury. The whole of this may be appropriately called the cold part of the stem. It is obvious that the corrections to be applied are specially important when the tem- ))eratnres of the bulb are high and the air is employed originally under small pressure. It is therefore expedient to derive the rigorous expres- sion for temperature in terms of all the variables involved, and from this to derive a safe practical form by simplification. The full expression in question introduces variables which may be symmetrically put as follows: h 11 V a t T v /* t' T' V" t" r£ti where h is the tension of the gas at the lower temperature, t of the bulb, and t' and t" of the variable and cold parts of the stem ; where H is the tension of the gas at the high temjierature, T, of the bulb, and T' and T" of the variable and cold parts of the stem ; where v is the vol- ume of the bulb and hot stem, v' the volume of the variable stem, and v^ the volume of the cold stem, all at zeio degrees; where or, finally, is the coefficient of expansion of the gas, and ft the coefficient of expan- sion of i)orcelain. The relation between these variables may then be rigorously expressed by the formula « ;.L±A^ "V^P'V 77^+/^^' iMf^^-M ' A here the symbol 2* denotes that similar expressions occur additively v' v" v'" for each ^j' ^> \«- • • • j to be considered, two of which, however, have been deonied sufficient, (813) 190 MEASUREMENT OP HIGH TEMPERATURES. Ibull.64. The equation simplified, — ^To simplify tiiis formala we replace ^ rx — } by /io, or the tension which would be observed if the bulb were placed in melting snow. Equation (1) then becomes, after solving for T, T=--^ri?+Z- (2) where 2 stands for the whole bracket [ ] of equation (1). This equation is still rigorous, but it is very inconvenient for calculation. An equally rigorous but much more serviceable form is obtained by introducing T into the corrective member coefficiented by 2:. In this way equation (3) results ^= sS-i-;® [' + y-t^3 (" a form which is still rigorous, but may be conveniently used in practice with any desirable degree of approximation, as will presently appear. In equation (3) 2 has the form t? L l+af 1 + afj t? L 1 + o(T' 1 4- at" J ^ ' v' which may be further simplified. Fortunately ~ is very small, for the mean temperature T is only determinable with rough approximation. I will define r' by the equation and then use r in a simplified form of 2. In the second term of the form (4) T^ = f' very nearly. If, finally, il— /' or «'' and jp'', respectively, and tJ© the zero volume of this set of canals above the fiducial mark. " Length ^ and *' Diameter" refer to the porcelain stem : Table 46. — Compensator volumetry. Ko. I V P 1 LfDgtb. Diam. CM. 1 Remarks. 1 1 ec. ein. Rg. ec. 1 em. a 0.30 77.49 1.7 0.8 The repetition of this series leads to practically tlie same result. 2.30 38.98 a 0.70 8.50 60.94 30.32 1.6 0.8 a 1.05 5.51 67.40 22.27 1.8 0.8 a 1.67 9.U0 48.21 15.42 1.9 0.8 a 0.27 10.50 76.46 8.31 1.7 0.8 > |......... b 0.30 15.40 76.50 15.48 3.46 32 0.8 h 0.50 15.40 75.16 15.60 3.40 32 0.8 1 1 1 o.rj 3.65- 75.40 30.65 2.35 40 0.8 1 1 0.40 68.69 2.28 40 0.8 3. CD 30.78 1 1 6.00 31.13 2.39 40 0.8 1 New adjustment i 1.02 76.59 1 1 8.62 23.90 2.43 40 0.8 1 1 1.03 76.59 . 3.85 32.75 2.03 30 > 0.8 Do. 0.48 76.65 1 1 0.58 76.03 1.91 36 0.8 1 1 4.C8 30. 57 i 1 1 1 (848) l*AJtUil.l PORCELAIN AIR THERMOMETRY. 195 Table 46. —Compensator vo^umetrjf— Continued. No. 1 V p. • ro Lenjztb. Diam. Kemarkrt. r CO. cm. Sg, ec. cm. em. 2 0.32 4.46 76.02 28.80 2.20 40 0.8 4.50 28.87 2.16 40 0.8 1 O.SO 78.13 3 1 0.85 4.45 75.85 28.44 \ 1.31 40 1.0 1 5.44 21.80 1.47 40 1.0 1 0.65 81.05 4 5.20 1.20 29.66 79.20 1.20 40 1.0 1.20 79.12 1.21 40 1.0 8.23 20. 16 0.30 53.89 1.06 40 1.0 New adjastmeut. 3.44 16.28 3.50 16.39 1.11 40 1.0 • 0.22 56.85 1 3.54 31.37 1.16 40 1.0 Do. 0.80 75.13 1.65 38.23 0.55 Platiuuni capillary tuben ami gltiss fttop-cock, with- out porcelain stem. 0.52 78.55 2.15 80.68 0.52 0.52 7a 61 1 1 1 0.13 76.17 0.52 I Platinum capillary tubes ' and {;I.ia4 Htop rock, with- out XMirrelain stem ; new utijustmcnt. 1 1.82 21.19 ^ 0.20 60.54 0.49 i 1.60 23.03 I a 35 1.10 31.85 75.82 0.53 Do. 1 The errors in tbese results are iibout O.l''^', and they are easily re- ferred to microscoi)ic leaks, to variations of temperature, and to the possible occnrrence of moisture in the stems. From these data it appears, moreover, that the internal volume of stems O.S*'"* thick is not necessarily smaller than the internal volume of stems 1.0*^°* thick. Hence the observed differences of volume between the divers stems are largely due to internal fissures, such as can not be detected, except by breaking the stems. It is interesting to note that the volumes measured vohimetrically are not more than twice t^s large as those measured by weight calibration. Hence the suiwrior limit of the errors in Tables 44 and 45 is not more than double the values there given. Errors of measureniait in general. — The degree of absolute accuracy with which the divers quantities ho, H, a, /i, ^' , ?— , must be measured in (849) 196 MEAHUREMENT OF HIGH TEMPERATURES. [ni'LL. 54. order that the efifectou Tinay not exceed 1 : 1000 follows easily from the equation of errors dx T 6x= (IT 1000 (12) From this the following six special equations resalt, equations which are approximate and put in such forms as may best facilitate the com- put4ition : a—fi 1000 tfflr= — [a-/3(\+aT)Y 1000. « ■ (13) ■ • (14) (15) 66= l«-M(l+«'2')J* g, r' \ l + a^T 1 '(:-)= l+fiiT 1000 . (l+aT) ■ ■ (16) (17) »// ^G)= _ 1 + rW" 1000 . vl + ^^^) (18) If into these equations we introduce ho=l^"% the value which obtains in most of the examples below ; if, moreover, a=0.00367 and /!^=0.000017, ^''=200, then formuhe (13) to (18) lead to the following tabular compar- ison. In the table both the absolute values of the errors Sho^ 6H, 6(i^ h ^\ zr )j which give rise to an error of T^/IOOO in the result, as well as the relative errors Sfi/fi^ 6 y ■ jj , and d ( )/ are fully computed for a series of values of T. Table 47. — Comparison of divers errors ichich effect iht result by I : 1000. t iho 6H 6fixl(fi 6^ :> 10« ^QxlO. r' < t V V o em. em. 1 1 i 100 -0.004 0.006 2.61 860 780 0.150 2.2 0.184 500 -0.010 0.028 1.27 , 680 380 0.074 1.7 0. 1 80 1,000 -0. 012 0.056 0.76 610 230 0.044 1.6 0.051 1,500 -0.013 0.083 0.53 : 580 170 0.031 1.5 0.039 Inasmuch as Ad must be measured to 0.01*'" it is quite obvious that corroborative readings before and after heating are essential, and that (850) BARU8.T PORCELAIN AIR THERMOMETRY. 197 tbe air thermometer duriog the intermediate measurements must be perfectly tight. Since the error decreases proportionally to ho, tjfie additional accuracy of greater zero tensions does not compensate the hurtful effect of high internal ^pressures at high temperature. Hence low pressures are preferable. Regarding jff, it appears that rise or fall of temperature must not be so rapid that the retardation due to flow of gas through the capillary tubes maintain greater differences of press- ure than (^.03*=" to COS*^"* of mercury. A good cathetometer presup- posed, it is not difficult to measure both Jio and JJ with the accuracy here called for. • Under most favorable circumstances the error of T is as large as the error of a, a result which equation (15) approximately shows. The value chosen, 0.003665, is Begnault's^ constant-volume value, and has been found experimentally for the interval 0^ to lOOo. The use of the same coefficient for temperature indefinitely high and for all tensions* is to some extent arbitrary. The error thence resulting may be esti- mated at as much as one-half of one per cent. The convenience with which the constant pressure method is available for measurements with gas differing widely in normal density is one of its most valuable features. The desideratum of an elliptic revolving muffie for the com- parison of the gas thermometer data of different gases, when the tem- perature of the same environment is measured, has been suggested. The unusually small coefficient of cubical expansion /f=0.000016 to 0.000017, which MM. Deville and Troost found for the porcelain of Bay- eux, makes the necessary accuracy of the coefficient /3 sufficiently at- tainable. The table shows that even in extreme cases, T=l,500o, an error of 3 per cent, in /3 is not serious, while the expansion coefficients of the metal and glass parts of the air thermometer need not be dis- tinguished from /3, because these parts are almost negligible here. This exceptionally small value of y^ is, however, only admissible in the case of thermometers which have frequently been heated. In the case of new thermometers these desirable qualities are vitiated by the occur- rence of permanent expansion for each heating. In comparison with /3 this permanent expansion (permanent din^inution of density) is un- fortunately enormously large, aggregating in the first six heatings, for instance, as much as 1.5 per cent. Whenever temperature increases too rapidly the temperature, and hence also the volume of the bulb, is larger than corresponds to the mean tempernture of the gas. The re- verse of this takes place on cooling. Conformably with the numerical results on page 197, Table 47 shows that — may be aff'ected by an error of almost twice its own magnitude V without seriously bearing on T, even in unfavorable cases. The impor- tance of , however, increases rapidly as T increases, and must in un- 1 Regnault: Memoires de rinst., vol. 21, 1847, p. 91 ; ibid., p. 110. « Cf. Literary Digest, pp. 36-38. (851) 198 MEASUREMENT OF HIGH TEMPERATURES. [BULL. 54. favorable cases be kuowii within 4 i>er cout. These results are also in keeping with Table 45, above. Fortunately it is feasible to measure // - - with the accuracy here required, as well as to sufficiently exclude the effect of temperature. A careful survey of the sources of error just discuRsed shows how ex- ceedingly difficult the measurement of high temperatures, with an accu- racy of 1 : 1000, really is. Quite aside from these discrepancies and the arbitrariness of a and /?, the lag error, the environment errof, the moist- ure error, the error du« to the permeability of porcelain and to diffusion of some gases through it, and the error of unknown flaws, have 3'et to be discussed. In the face of these serious difficulties I was therefore pleased to find that greater harmony prevails in the established data for high temperatures than there was reason to anticipate at the outset. I may state here that a more rigorous discussion of errors is to be made in treating the constant- ])ressiire method, since this method is very much better adapted for high- temperature measurement than the present one. I will (p. 228) give the methods of allowing for all arbitrary errors and such as are not considered here. k CONSTANT-VOLUME THERMOMETER — EXPERIMENTAL RESULTS. Earlier results. — The measurements were "commenced with the forms of bulb shown above in Fig. 32. These bulbs are not glazed internally, but consisting of but a single piece they can be manipulated with greater facility than the others, in-which soldering must precede the temperature measurement. To obtain some idea of the availability of the unglazed bulbs, I made a number of measurements of the boiling point of water. Examples of the results obtained are given in Table 48, in which H and ho are the tension of the air at 100^ and at 0^ in centimeters of mercury. It is to be remarked that h is here directly obtained by surrounding the bulbs with melting snow for many hours. By way of comparison, the same temperature T is also measured by a glass air thermometer. Table 48. — Moisture error of unglazed buJba. 1 "So. 1 ... - ^- ho H T Keniarks. ! (;1uam: cm. em. re. ' Xo. 1 . . . . 76.70 104. 47 100 : VorcolaJn : No. 1 .... 73.50 141.90 256 Bulb Dot Hpecially dried. Xo. 2 . . . . Xu. 3 72.40 7C.46 115.00 119.58 jgo ( Both bnlbs diietl by rcpealexl oxhAus- 155 ") ^^**° after calibration with water. . I Bnlb at 100° duriiiji: drying. Xo. 4 1 1 72.02 102.9« 115 Bnlb carefully dried by repeated ex- liquation with mercury air-pump. Bnlb and ntem at lOO^. (852) BABUa.1 PORCELAIN AIR THERMOMETRY. 199 The results of this table are startling. They seem to show that bulbs not glazed interually are worthless for temperature measurement. The error Is very largely due to the presence of moisture in the bulbs.; prob- ably also to the condensation of air in the pores of the unglazed ])orce- lain. An explanation of these results can be given by equation (13) and Table 48. This consideration exhibits an important principle, so far as drying by exhaustion is concerned, and may therefore be made here. Bulb Ko. 4, which is most carefully exhausted, need alone be discussed. It appears that the value of 6 H and 6 ho, which give rise T to an error of j^n, are approximately dll — 2.7*'™, and 6)1^=: l.S'^"'. No^, after a mercury air-pump has been much used for drying, moist- ure is apt to show itself in the receiver, after which the exhaustion can not be carried further than 2*"° at ordinary temperatures. Hence it appears that unless the exhaustion be very frequently repeated a ten- sion of aqueous vapor equivalent to about 2**" of mercury at 100° may &il to be removed, an amount nearly sufficient for the discrepancy in Question. It is to be noted that like errors in H and h^ do not compen- sate each other. The amount of water thus remaining in the i)ores of the cold bulb is about 4""^. These results point out the desirability of perfect exhaustion and the necessity of keeping the air-pump dry. In view of the enormous discrepancies cited in the last table, the unglazed bulbs were discarded. Some years after, however, when the difficulty of soldering porcelain had been tried in many experiments, I resolved to test these unglazed bulbs again, with a view to perfecting them. In the first place it is obvious that if, instead of determining Ao directly with melting snow, this datum be calculated from measurements of h made at ordi- nary temperatures (250), better results will probably be obtained, since the small impurity of vapor may in the latter case be more accurately treated, like a gas. Moreover, care was taken to dry the bulbs at red heat prior to using them for air thermometry. Table 49 contains re- sults for bulbs thus dried, all unglazed internally, except No. 1, which is the soldered form (Fig. 33), glazed internally. Table 49. — Moisture error of unglazed hulbs. No. H Porcelain : cm. No.l 75.8 Na2 75.7 Na3 63.6 Na2 35.7 No. 3 48.5 N0.4 76.3 N0.4 17.26 K T Remarka. cm. °a 04.2 00 04.3 00 78.0 102 45.7 104 61.1 102 07.0 102 21. 6U 101.1 CathctoinoifT measarement. (853) 200 MEASUREMENT OF HIGH TEMPERATURES. IniTLL. M. These results are snch an enormous improvement on the discrepancies of Table 48 that it seemed expedient to endeavor to farther investigate the behavior of these iustrnments at high temperatures. If under these conditions the bulbs show no greater variations than is in accordance with the above data, the further improvement of the bulb preseiits it- self emphatically. Values of high temperatures sufficiently approximate for the present purposes are obtainable by the method investigated in Chapter II, where apparatus for calibrating thermo-elements with known boiling points are described. It seemed especially desirable to make this high-temperature comparison in order that some definite pre- liminary notion of the degree of accuracy of high-temperature data in general might be independently obtained. Examples of these re- sults are given in the following tables, 50 and 51. The first of these (Table 50) contains a comparison of the calibrated thermo-element and air thermometer made in the large gas-muffle furnace described on page IvSl. The junction of the thermocouple having been tied with asbestus wicking to the equatorial parts of the air thermometer, the whole bulb was thereupon surrounded with a non-conducting jacket of carded asbestus, from one to two inches thick, inclosed in a cylindrical asbestus box. Both the thermo-electric and the air thermometer meas- urements were made in time series, with one observer at each instru- ment.^ In this way the rate of heating or cooling of the furnace appears among the results. As usual /to is the (calculated) zero reading of the air thermometer, 11 the corresponding reading at the high temperature T, and at the time given in the same horizontal row. Again, t is the temperature of the cold junction of the thermoelement, e the corre- sponding electro-motive force, in microvolts Tj^ and T^ the calculated (thermoelectric) temperature when in the first case the calibration is carried only as far as the boiling point of mercury, in the second case when carried as far a« the boiling point of zinc. Tj^ and T^ are the results of graphic interpolation, as explained in Chapter II, page 114. Table 50. — Comparison of air thermometer and thermo-element. Bulb No. 3 : /!,.=: 26.6"» 1 Time. 1. hoiin. Thermocouple K 0.36. n T 1 t mierovolU. Tki, T^ Time. hourg. cm. 0(7. <^0. ^0. 330.1 66 12.46 24.7 650 97 97 12.52 464.3 207 .53 .8 1530 19G 196 .55 637.9 389 .57 .8 2220 264 * 268 .56 705.7 462 .60 .9 4270 443 460 .61 759.4 519 .63 25.0 6400 696 636 .71 817.1 581 .66 .3 1 7260 655 705 .79 ^ Dr. Hallock kindly asaisted me in this series of measurements. (854) BABU8.1 PORCELAIN AIR THERMOMETRY. 201 Table 50. — Comparison of air thermometer and thermo-elemenU — Cont'd. BnlbNo.3: A«=26.6"«' erm 847.9 , 898.7 i 928.7 965w5 ! 1017.3 107a 5 1 1107.0 , 1150.6 I 1170.8 I 1187.8 ' 1198. R I 1202.8 I 1203.3 ! 1202.8 1 1109.8 i 1126.5 1064.3 I 979.3 i 934. 8 I 859.3 ' 79813 721.9 678.4 633.5 691.7 655.4 ' 522.7 ' 483.9 ' 462.9 I 613 670 700 741 797 863 896 942 973 984 996 1000 1000 1000 007 916 848 756 706 626 561 478 433 385 340 302 267 227 206 TiiHO. hour*. .69 .74 .79 .83 .90 l.Ol .08 .25 1.35 '*2 .50 .58 .67 .75 Oas 1.81 I .87 .92 .07 2.01 .07 .13 .19 .27 .35 .43 .53 2.63 .74 .91 Thenuo-oouple No. 36. t 1 Tkff Ilm Time. or. mieronolU. OC. oO. hourt. .4 8490 782 792 .86 .5 8860 756 821 .89 .5 9260 777 846 .94 .7 9710 802 878 1.00 .9 lUUO 826 906 .07 26.3 10630 850 933 .17 .4 10760 8G4 950 .22 27.4 11570 908 1000 .45v 27.6 11630 911 1006 1.60 . t 11700 915 1010 .53 .9 11840 924 1017 .61 28.2 11970 928 1026 .70 28.4 120G0 934 1030 .76 1 of furnace Hhut off 1 .77^ 28.9 107M) 864 961 1.87 29.2 9930 815 893 ' .91 29.3 9130 769 838 .96 29.4 8520 733 794 .08 29.4 '7570 675 727 2.03 29.5 7060 640 686 .06 29.5 6500 610 651 .09 29. r. 0100 58i 621 .12 29.5 6170 515 538 .21 29.5 4700 476 406 .26 29.4 4310 445 461 .30 29.4 3980 421 430 .35 29.4 3400 372 384 2.44 29.4 3140 348 358 .48 29.4 2860 324 332 .54 29.4 2810 274 277 .68 29.4 2000 245 246 .79 29.4 1790 226 226 .87 29.4 16G0 214 214 .93 The following comparison (Table 51) of the data of thermoelement and air thermometer was made in the revolving maMe, described on page 181, The simple round bulb (No. 4), not provided with a central tube, having been properly adjusted, the thermo-electric junction was placed nearly in contact with it. The table contains three independent series (855) 202 MEASUREMENT OF HIGH TEMPERATURES. (BULL. 54. of measurements, and nomenclature used is identical witb that of the foregoing table: Table 51. — Comparison of air thermometer and thermo-couple. Bulb No. * »• Thermo-couple No. 37. T Time. t < 2\i T„ Time. (a) [A«=16.74'-l em. oa hourf. OO. microvoltt. oC. °C. hotirt. 82.2 1115 , 1.57 25.3 12920 980 1082 1.53 88.9 1238 1.85 25.8 14780 1073 1196 1.73 89.2 1244 1.03 27.3 15430 1102 1233 1.00 89.3 1246 2.03 27.3 1 15600 1115 1249 2.05 ib) lfco=14.70'»1 «2.C 923 2.27 ' 26.3 10480 850 930 2.22 64.2 954 2.35 ! 26.5 11020 878 972 2.83 72.5 1118 2.53 27.0 12250 M4 1045 2.47 76.6 1202 2.62 27.3 14O0O 1034 1150 2.60 77.3 1218 2.65 27.8 14760 1072 1195 2.72 78.6 1244 2.73 28.2 16060 1085 1218 2.82 79.1 1254 2.80 28.2 14970 1081 1206 2.87 79.1 1254 2.82 28.5 14870 1075 1201 2.92 78.8 78.4 1248 1240 2.85 2.92 ( Sas of farnaoe shut c >ff. 72.8 1126 8.03 29.0 12930 980 1085 8.03 66.8 1006 8.12 29.5 10710 861 945 3.17 62.8 927 8.22 29.6 10090 827 904 3.20 67.8 819 8.80 80.0 9040 765 83d 3.32 51.4 704 3.47 30.6 7690 683 735 3.48 46.3 603 3.68 31.3 6400 604 644 3.68 42.0 i 519 3.92 31.8 5340 524 551 3.92 36.0 422 4.27 81.8 4130 430 449 4.27 32.5 337 4.68 31.8 3140 350 359 4.70 24.8 , 188 1 1 [ft«=15.68«-) 77.0 1115 2.00 29.0 14170 1042 1160 2.00 77.4 1122 .03 29.0 1 14270 1046 1166 2.03 68.5 957 .18 29.0 10770 865 948 2.17 62.7 659 .53 29.0 : 7090 644 690 1 2.50 The results of these two tables, 50 and 51, may best be compared graphically by regarding the various values of temperature as functions of time. This has l>een done in the chart, Fig. 39. The curves a, b^ c correspond, respectively, to T, T^, and Tj^ of Table 50 ; the curves A, fc, ♦ to T, T^, T|^, of Table 51, respectively ; the curves /, g^ and m, n to T (856) I I50C HOO j ' i I. i i ■\ ' . . » .. .■^* f ■ I ^ •V. *\ .1 I > . I ■f 9 o ' .'n 4 I' <1 BARC8.] PORCELAIN AIR THERMOMETRY. 203 and T^ of the same tablc^. The curves d and e are supplied by way of example, anolation. The extrapolated temperature T^g differs enormously at high temper- atures from its air-thermometer value, the latter being the greater. Since below 900°, r< T^, the discrepancy can not be referred to friction of gas in the cainllary tubes, the effect of which would be of the oppo- site sign. The only cause which would tend to cool the air thermometer at a greater rate than the thermo couple is the effect of the entrance of the air above the meniscus of the manometer, while the mercury is gradually moving upward from a lowered i>osition into contact with the fiducial mark. Or, finally, the error T^T,^ may indicate superheating in the calibration work. It is by no means the object to furnish in this place more than a sta- tistical diagram, as it were, of the degree of accordance, which the high- temperature measurements made in widely different ways, present. When comparisons are made in the Bunsen muffle the ascending val- ues of T„, exceed the descending values of T,« for the same T. The ascending and descending values of T,„ in case of comparisons made in the revolving muffle are nearly the same. This is a pretty fair test for identity of environment. Nevertheless, if all values of T^ obtained be laid off as functions of T, the band or pathway thus obtained is in some (857) 204 MEASURKMENT OF HIGH TEMPERATURES. [iu:LL.S4. instances nearly lOOo ^j^e and the boiling points of zinc fluctuate be- tween 9250 and 9950. Later results. — Following the suggestion of the results contained on pages 199 to 204, 1 made the following series of additional comparisons. The bulb used is still the non-re-entrant form, not glazed internally. Great care was taken to dry it thoroughly by heating the bulb to lOQo, and then exhausting the air to a few tenths millimeter. After being treated in this way the bulb was filled with air, dried over anhydrous phosphoric acid. Tn the last two series Iiq is calculated from the tension observed at lOQo. Special care was taken with the cathetometric meas- urements. The series of temperatures is ascending. The influx of gas is gradually increased by means of a graduated stop-cock, and the cali- bration measurements are made after each increment as soon as the temperature has again become stationary. In this way not only may any number of degrees of constant temperature be obtained, but the mean rate at which temperature increases may be reduced as near zero as is desirable. If therefore one observer^ notes the instant of contact between the upper meniscus of the manometer and the fiducial mark, the other observer may note the corresponding cathetometer reading of the lower meniscus for the same instant. From, a comparison of the following results as a whole I infer that in proportion as the tem- perature of the muffle increases, equality of temperature for all points of its inner surface more nearlv obtains. This is due to the fact that at high temperatures its heat conduction is better. For low temperature calibrations it is therefore advisable to use a muffle cooling from red heat in a closed furnace. In the tables ^m has been calculated for ^=20^. The actual temperature {t) of the lower junction is given in Table 52 for each case. Table 52. — Comparison of air thermometer and thermo-couple. Ao = U.66«. Bulb No. 4. Thermo-couplo No. 37. U em. 27.35 30.25 31.68 33.25 34.32 34.32 41.47 42.33 48.49 49.90 iSO.Se 57.80 0(7. 241 297 324 354 375 375 512 529 048 678 694 831 Time. Jioura. 2.78 2.88 2.99 3.14 3.35 3.42 3.73 3.78 4.00 4.07 4.11 4.31 e» Time. 28.0 2&0 28.0 2&0 27.8 27.8 27.8 28.3 28.3 28.3 28.3 28.3 microvolts. I 2545 i 2941 { 3060 3283 I 3792 I 3780 3780 ' 5475 5820 7132 7706 8015 houn. 2.78 2.84 2.90 2.97 3.40 3.43 3.45 3.68 3.75 3.93 4.02 4.08 ^ Mrs. Anna H. Barus assisted me in this work. (858) 1 PORCELAIN UK THBRHOHETBY. 205 Tablb Iht. — CoMjMrtMa of mr thermometer oad Ikermo-eoiipU. — Cont'd. k> = U.W-. Bolb»o.4. m»nn8.5a 845 3. 28 33.0 13021 3.73 se.«i 8S3 3.4S 33.3 183 SS.4II S82 3.00 33.S 13127 3.02 ae.40 2. 70 33.8 11107 M.88 1049 3.87 33. G 11077 4.05 ».m ».»8 31.3 4.12 7103 1113 4.05 31.3 mil 4.17 «.T2 U4» 31.3 1S732 4.22 75.68 IIM 4. IT 3i.i tiiSt 4.30 1200 4.22 34.8 13M8 4 42 T7.W 4.2S II. as 1245 4.33 1 mil 1M5 4.30 ™,47 1282 4 4* In spite of tbe care takeo with thexe obnervatiotiH tlie resnlts do not show the uuifonnity and accuracy expected; thisaiipears from a graphic representatiOD of the followlug correlative valneti, Table 53, takeu fitoui Table 52. 206 MEASUREMENT OF HIGH TEMPERATURES (BULL. 54. Table ^'3,— T and 620- I. ir. IIL T ^M T ; 1 T • '»o 250 2630 360 ' 4050 9C0 1138 300 3050 400 4400 995 1176 375 3700 450 4880 1080 1340 525 5800 470 5100 1100 1378 670 7860 550 6560 1130 1445 800 10400 600 7050 1180 1520 1016 12850 630 7350 1240 1610 1080 13800 702 P 730 8240 1260 1628 8860 1 820 10000 847 10360 1000 13000 1050 18420 1100 14540 1150 15060 1200 15640 j 1250 15900 1 f The values of temperatare are small relative to the electro-motive forces. This would result if the stem error applied is too small by an amouDt quite withiii the range of possible error, but it is more likely that the thermo-couple is here at a temperature above that of the air ther- mometer; iu other words, that the environmeuts are not identical. A reverse of this takes place on cooling; hence the use of a simple non-re- entrant bulb for comparison is not at once permissible. It is necessary if the results are to be uniform and comparable, that both bulb and ther. moelectric junction be not only contiguous, but be enveloped in some thick non-conducting substance. Such additional appliance is objec- tionable, since it interferes with quick and facile manipulation, and at high temperatures is fused into the glaze of the bulb in a way that en- dangers it. Mere contiguity of the junction and the bulb, even in case of a revolving muffle, is not a sufficient guaranty for the accuracy of the calibration results obtained. Digression, — Before resolving to change the form of the bulb, I made another series of experiments, which hav^ an ulterior interest, inasmuch as they are made with the soldered bulbs, glazed both within and with- out, which are described above, p. 1 75. It was also expedient, if not nec- cssaiy, to change the method of measurement, and in the following results. Table 54, the constant- volume method is replaced by the con- stant-pressure method. The data are given in a way that will be fully explained in the next paragraph (p. 217), and it is here only necessary to refer to the time series of T, the temperature of the bulb, and of ej©, the corresponding electromotive force. Corresponding values of €20 and (860) fiARVB.] PORCELAIN ATB THERMOMETRY. 207 T arc collected in Table 55, and obtained as before by graphic interpo- latiou. The results are inserted here because of the non-re-entraut form of bulb employed. Table 54.— ComparUon of air tkermomtiter and tJiermO'OOupU, In f^lazed bnlb No ^\?Z 282* 20- Thermo-ooople No. 87, Vi 1 1 1 -»• 1 ^ Time. 1 houn. 1 1 e» 'microvolt. 1 Time. hourt. Oan- cock. cc. •a em. • •c. •0. 147.0 24.3 76.46 333 1.12 i 22.4 8039 1.05 2 140.7 24.3 76.40 345 1.17 22.6 3534 1.22 2 154.3 24.3 76.46 366 1.28 22.8 3743 1.34 2 157.0 24. G 76.46 379 1.38 23:1 3906 1.48 2 160.4 24.8 76.46 396 1.55 23.6 4110 1.78 2 163.1 25.5 76.46 400 1.88 23.7 4104 1.02 2 163.4 192.5 25.4 26.1 76.46 76.46 411 621 1.08 2.28 . .. . ...A 8 24.8 7160 •• 2.83 196.0 26.2 76.46 655 2.37 84.9 7455 2.42 3 201.9 26.6 76.46 716 2.78 25.4 7926 2.67 3 202.5 26.7 76.40 722 2.84 2S.8 8076 2.81 S 211.7 26.0 76.46 841 3.12 26.6 10270 3.17 3.5 216.0 27.0 1 76.46 907 3.33 26.8 10621 3.80 3.5 216.6 26.0 76.46 910 3.47 27.0 10748 3.42 3.5 217.4 27.1 76.46 931 3 67 27.4 10040 3.68 3.5 210.0 26.0 76*46 960 3.82 28.1 11602 3.87 3.7 220.7 26.8 76.40 994 3.<)8 28.3 11793 aoG 3.7 222.2 27.1 76.40 1019 4.13 28.4 12052 4.05 3.7 223.0 27.0 76.40 1030 4. 25 1 28.6 12364 4.20 3.7 223.2 26.0 76.46 1041 4.40 j 2&6 12170 4.37 3.7 220.0 20.5 76.40 985 1 4.58 29.1 10480 4.65 • 215.0 26.0 76.40 903 4.68 i i 29.3 0563 4.73 210.0 25.8 76.46 828 4.78 29.3 8807 4.81 205.3 25.5 76.46 767 4.87 29.3 81S5 4.88 200.2 25.3 76.46 707 4.97 i 29.4 7339 5.03 189.8 25.0 76.46 602 5.20 29.1 6404 6.18 180.8 25.2 76.53 528 5.42 i 29.0 5049 5.33 !3 9 170.0 25.2 76.53 452 5.C8 1 28.8 5009 5.C0 73 160.2 25.1 7a 53 396 5.03 28.7 4275 5.73 154. 8 25.0 76.53 360 6.05 28.0 3835 5.88 145. 3 24.8 70.53 325 6.30 28.6 3589 5.08 140.4 24.8 78.53 307 6.42 ' 28.6 3344 6.08 129.8 24.0 76.53 267 0.68 28.4 2970 6.27 124.9 2J.7 , 76.53 251 6.80 , 28.2 2750 6.38 1 27. G 2325 6.65 (861) 208 MEASUREMENT OF HIGH TEMPERATURES. [BULL. 54. Table 55. — T and c-o from Table 54. [Noii-re-entraiit inglaxed bulb No. 2; themio-coaple No. 37. J ! T 1 fM microvolt. 1 T i 1' micro roll. T 1 tn 1 t. oC. ">€. microvoU.'. 333 3240 ' 007 , 10C50 767 8270 345 3360 010 10800 i 707 7550 366 3040 i 931 11000 602 G320 370 3780 004 11860 528 5320 300 4000 1010 12220 1 452 4430 400 4100 ; t 1036 ■ 12400 : 396 . 3710 411 4110 7300 369 3410 1041 12600 655 1 325 2040 716 6040 003 10150 307 2720 722 8100 ' 828 9100 267 1 2300 1 In the upgokig series, in which observations were made only daring periods of very constant temperature, the values of electro- motive force are normal in comparison with values of temperature. The boiling point o/zinc, for instance, is fixed at 930o. i,i the down-going series therraoelectromotive force is too small, as usual. The eftect, however, is possibly exaggerated by the great diflBculty of making these bulbs absolutely tight. Nor is it ])ossible to estimate the leak efiect as a fhuctiou of time, for the capillary canals change with temperature and even by accidental disturbances. Difficulties such as are here described led me to the construction of the re-entrant form of bulb, in which, by a simple device, they are wholly obviated. This will be shown at length in the final section, which follows. I have purposely given a full series of data in Tables 50 to 55, in order to bring before the mind the extreme difficulty en- countered in making comparisons between the thermo-couple and the air thermometer, when the conditions to be met are accuracy and expe- dition. CONSTANT PRESSURE AJR THERM0:METRY — APPARATUS. The above data were investigated in the rational endeavor to adapt Jolly's very convenient form of air thermometer to high- temperature measurements.^ To do this I found it desirable to use low-pressure (< 1 atmosphere) manometers, so that at high temperatures, when porcelain shows a tendency to become viscous, the pressures on the interior and on the exterior of the hot bulb may not differ by an amount sufficient to de- form the bulb seriously. But while on the one hand this can never be perfectly accomplished, the difficulty of maintaining the air in the bulb and manometer at an invariable low pressure makes this instrument un- usualiyliable toerrorsoraccidentson theother. In the constant-pressure method of air thermometry, all hurtful excesses of ]>re8sure on the bulb I Weiuhold, Erhardt, and Schertel tried it before (cf., p. 33, 34). (862) BABUB.) PORCELAIN AIR THERMOMETRY. 209 may be almost wholly excluded, the pressure choseu being, of coarse, that of the atmosphere. In this method, however, the volume of the bulb must be accurately kuown, a datum which is only of secondary importknce iu the constant-volume method. Again, the above data are obtained with spher- ical bulbs of the non-reentrant form. The diffi- culty experienced in obtaining a degree of satis- factory accordance in the various series of data is due to the fact that the environments are not identical. Hence in the following experiments the re-entrant form of bulb (Fig. 32) will be used, in which an identical exposure has been as nearly as possible realized. It will scill be necessary to op- erate with bulbs not glazed internally. For final work bulbs of the re-entrant form, constructed in accordance with the Deville and Troost plan (Fig. 33), so as to be easily glazed internally, are avail- able. A very convenient and simple apparatus for constant-pressure air thermometry is;?ivenin Fig. 40, iV actual size. The details of construction are very similar to those shown in Fig. 30, and it is therefore only necessary to indicate the essential I)oints of difference. In the present instrument the platinum capillary tube A, the further end of which communicates with the air- thermometer bulb, is soldered with resinous cement into the top of a long cylindrical tube, B G. The length of this tube is at least 150^'"» ; it is accurately grad- uated in cubic centimeters, and the total capacity is about 300*^". In my apparatus the tube B C was closed below with a rubber cork, and this end then inserted with plaster of Paris into a suitable rest or foot. By removing the fbot and the cork the tube admits of being cleaned, an operation which, for the case of imperfectly pure mercury, is sometimes necessary. Practically the tube is closed below, but it is provided at a short dis- tance above its end with a horizontal tubulure, D jE7, to which a cloth-wrapped rubber hose, E FOj is attached. The upper end oi E F O communi- cates by means of a three- way cock, fl, with a large cylindrical vessel of mercury, K L L, The cock iff has a lateral tubulujre, A, through which mer-i Bull. 54— -U (863) Fig. 40. donstantpressant ftir«thorbi6io^(er. i 210 MEASUREMENT OF HIGH TEMPERATURES. [bull. 54. cury may be withdrawn either from the tube B C or from the reservoir K L L, The latter aud the cock H may be uuscrewed from the steel piece inserted into the hose at O in the manner shown in Fig. 30, above. This system is practically a U-tube, one of the arms of which may be varied in height or length at pleasure. For this purpose it is attached to the manometer stand, already described. (See frontispiece under B,) B C \» Hxed to one of the uprights with its weight mainly resting on the foot at 0. The reservoir K L L aud the cock H are fixed to the slide, which may be moved at pleasure up or down and clamped in any posi- tion on the second parallel upright of the manometer stand. The slide is conveniently provided with an ordinary micrometer screw, by which a finer adjustment is obtainable. Enough mercury is introduced to just fill the tube B C and leave a well-defined meniscus in the reservoir K L L. Moreover, the dimensions ofKLL are such that when it oc- cupies its lowest position, and the mercury is almost completely out of the tube B C, the reservoir may be about filled. Measurements are made with the cathetometer, which in this case, however, has no other purpose than to indicate identity in the level of the menisci in B C and KLL, The pressure is then that of the barometer, which may be con- veniently suspended from the same stand. (See frontispiece.) Volumes are read oflt* directly on the glass tube B 0. Two sensitive thermome- ters at the lower and upper parts of this tube, respectively, show its temperature. This is the form in which the apparatus was used. It will be remem- bered that the chief purpose of the present memoir is to test the availability of methods. Whenever it becomes desirable to investigate data of extreme accuracy, it is, of course, necessary to surround B V with a jacket of water, so that the temperature throughout its length may be kept rigorously constant. Again, the increment of volume, corresponding to a given increment of temperature, decreases in propor- tion as temperature itself increases. Hence, if it be desirable to meas- ure high temperatures, a volume tube may expediently be chosen, of which the lower part is of smaller diameter than the upper part. Data for the construction of such tubes for any special purposes will be fully given in the tables below. Long capillary metallic tubes cool down the gas to atmospheric pressure before it enters the volumenometer tube B C. CONSTANTPEESSUEE THEEMOMETRY— METHOD OF COMPUTATION. The general equation. — Equation (I), on page 189, applies here as it did in the case above. The former simplification con- sisted in so conducting the measurements that A=0. The present (864) BABua.] PORCELAIN AIR THERMOMETRY. 211 experimeuts accomplish a similar parpose by making H=h ; for the valae of A is easily found as where Vi is the excess of the volume of the gas at the high-temperature measurement T over that at the low-temperature measurement tj and where Ti is the temperature of Vi . The older method therefore eliminates the volume factor ; the present method eliminates the pressure factor. If we expand equation (1) for the present case we find the following correlative variables : V t T f/ V T V, - T, where v is the volume of the bulb, v' the volume of the part of the stem along which temperature varies from T to f, v" , , . the volumes of the remaining capillary stem and capillary tubes of nearly constant temperature, F], finally, the excess of volume of gas at the high-temper- ature measurement typified by T, over that of low-temperature measure- ment typified by U Temperatures referring to the same volume are similarly accentuated. If for abbreviation and 2^HS=:2^-V Hf{T')--hf{V)'\ then equation (1) leads to the following value of T: H(l+^f{T,)yhf(t)+2 T=—y- - y — ^ — (2) This equation is rigorously true ; but it is unwieldy, and to be made practical must be simplified. The equation simpUjied. — Equation (2) may be easily put into the form H^kf(t)+n-Jf(T,)+a+aT)2 T= ^ y J .... (3). which for H=h, the condition underlying the present method, and for ^=/(«)-^'/(r.) W (865) 212 MEASUREMENT OF HIGH TEMPERATURES. IbuluM. an abbreviating expression, reduces to This is the form reqaired. It is nearly rigorous, the approximations having been inserted in the corrective member . It is perhaps inter- m esting to annotate that the rigorous form (2), under the simplifying condition H=zh reduces to the unique expression A few remarks on the practical method of using equation (5) are now in place. Equation (4) shows that f, the lower temperature at which measurement is made, furnishes the fiducial or fixed point of the air thermometer, t is obviously the temperature at which Fi=0 under the given barometric pressure &, of the day on which the measurements are made. Now, if at the barometric height B and at the temperature r one observes ri=v, then /(0=f(l+-4-j)/(r) (6) * where 2(r) is the total volume of the bulb and capillary stems as far as the zero mark of graduation on the tube B C. Equation (C) follows at once from equation (1) in the general form given on page 189, if we impose T=:T=T*= . • . Ti and t=-t'=t'^ • • • j tlie conditions given by the experiment. Equation (6) is therefore generally true. Usually h and -B, t and r differ but slightly and v is nearly zero. Hence, having measured r, B^ v, it is easy to find the value of ty which corresponds to the barometric height h of the day; and it is also easy to make allow- ance for any variation of barometric height occurring during the course of the experiment. These operations are simple and the corrections can mostly be made mentally. Mere inspection of equations (4) (5) (6) shows that it is expedient to calculate a table for the function /(^)==4^> ^^^^ *or glass and for porcelain, once for all. Such a table in which t varies from 0° to 3(P, in single degrees, will usually suffice. In this table, however, the data lo^/(^)> which is more frequently in demand, must also be inserted for the same range of t If the re-entrant bulb be used, the mercury thermometer is con- veniently inserted into the central tube while the bulb is in place in the revolving muffle. The stem of the mercury thermometer aboiild be (866) nARlTB.] PORCELAIN AIR THERMOMETRY. 213 SO long that the position of the thread may be seen. This furnishes r of equation (C). It is frequently convenient to make this measurement for unequal heights of the columns of mercury in the two arms of the manometer. In this case By of course, is the eifective tension of the gas. The difference in height of the menisci is read off by the cathetometer.^ Volumetry of btilh. — Equations (4) and (5) contain the quantity F, or the volume of the bulb of the air thermometer at zero centigrade. This may, of course, be measured directly, before the high temperature work, by calibrating with water. If, however, a bulb non-glazed in- ternally be used it is exceedingly difficult to dry it again thoroughly. Hence I have applied the volumetric method already utilized above in the case of stems. In the case of a manometer like the one described in Fig. 40 this method is applicable with great elegance, inasmuch as pressure can be varied over a large range and volumes read off with facility. In the following table an example of data obtained in this way is given. t?i and p are corresponding values of the volume of the gas in the manometer tube B G (Fig. 40), and of the pressure. Measurements are .made with the bulb and manometer in the air, and no thermal correction is applied : Tadlk 56. — Volumetry of hulh. Date. 1 P vo ce. ! em. ec. Oct. M 4.9' 75.88 279.6 122.2 1 53.73 4.8 1 75.93 280.1 122.2 1 1 63.77 Oct 15 3.0 i 75.65 281.0 120.2 1 53. 55 30.0 ; 75.60 280.9 120.2 ! 53.59 9.7; 73. 97 282.0 120. 8 1 53.56 1 6.5 , 74.82 281.3 , 120.8 53. 55 4.U 75.46 281.4 120.0 53.70 7.4 74.93 279.9 126.6 52.96 Oct 16 4.0 76. 2 1 280.1 126.0 52. 64 4.0 75.22 281.3 120.5 ' 53.41 3.0 75. 54 279. 9 120.5 1 53. 38 3.0 1 75. 53 281.3 I Mean »^ = 280. 73 ' MaDy operations may be simplified ]»y usin^ Laudolt and Hoerustein's physical tables ; Berlin, 1883 ; cf. pp. r> to 7. (807) 214 MEASUREMENT OP HIGH TEMPERATURES. [bull. 54. The variations of Vq here observed I was first inclined to attribnte to the difiicnlty of defining the volume of a bulb, the interior of which is not glazed; but they are due to thermal distarbauces. In order that the present method may be made to yield the best results the tempera, ture of the bulb and of the manometer tube B (Fig. 40) must either be rigorously the same, or the respective temperatures must be known. For, if 2v be the volume of the bulb and capillary stems at the tem- perature ty and if Vi and Fg be the two volumes read off on the manom- eter tube ^ at the temperature Ti , and if Hi and Ht be the pressures or gas tensions which correspond, respectively, to Vi and V^j then AT,) HiVi^mV, _ an expression in which if Ti and t differ by as little as a few tenths of a degree the factor f(Ti)//(t) can no longer be considered negligible. It will be seen below that 2 (v) must be measured with a degree of precision scarcely exceeding 0.02 per cent., i. e., to about O.V^ for the given capacity of bulb, if the absolute value of T is to be correct to one pro mille. But after many measurements, the further citation of which is here superfluous, I convinced myself that when due regard is paid to the temperature factor th ^ accuracy in question is attainable. /( Ti ) -h/tO is approximately 1-f a(t— Ti), in which form it may be easily applied. Errors of the approximations. — It is necessary to discuss the corrective member of the equation (5). 8 VIZ, M .. 1. ... ..t. i« .. . ^ ^ 8 —^ — -, or as it may be written with sufficient accuracy, —^ For practice it is best to write for this the equivalent form '_jl? — l^ and then to calculate a table from which, for each value of T, the value of this corrective function may be taken at once. It is usually suffi. cient to proceed as follows : The full form of the corrective function is o^^y^ {I' \/m-/{n]\. For those parts of the capillary stem whose temperatures are con- stant, /(T") and f{t'^) are practically identical. Hence the part of the stem along which temperature varies irom the high value to that of the atmosphere alone enters into the consideration. It follows that the last expression may be written ^^±^^- [AT') -At')]. BABU8.1 PORCELAIN AIR THERMOMETRY. 215 Even this correction is small, and for 1,500^ will not mnch exceed 5^. It is permissible therefore to pat Tss2T and to insert for t' a mean value. Table 57 is of the kind here referred to, and exhibits the valaes S for each value of T and for fs=15o ; v'/v is found by measure- ment to be 0.00043. Table 57. — Errors of thermofMter formula!. T S T 8 1 T ^0 S OC7 ■ 100 — 0.0 600 — 0.6 1100 — 1.8 200 — 0.1 : 700 — 0.8 1200 - 2.2 800 — 0.2 800 — 1.0 1300 - 2.6 400 — 0.8 1 900 — 1.2 1400 — 2.§ 500 — 0.4 1,000 — 1.5 1500 - 3.4 It will be seen by comparing this table, 57, with the similar one above (Table 45) for the constant- voluuie method that the errors here are very much smaller in magnitude. A result of this kind was to be antici- pated, and the occurrence of small stem corrections, added to the fact that measurements are made in such a way that the tension of the gas inside the bulb need not exceed atmospheric pressure, is the salient advantage of the present method of high-temperature measurement over the constant- volume method. Compemator. — In calculating the results of the last table no allow- ance is made for fissures or for the porosity of porcelain. Hence bet- ter results may be anticipated by using the compensator, though it always remains questionable whether the volumes of two nominally identical porcelain capillary stems are at all identical in fact. How- ever, it is only the part of the compensator along which temperature varies from the high value T to that of the room that need be identical with the stem of the air thermometer. The remainder of the compen- sator may have any (capillary) volume, which need not be exactly the same as the volume of the capillary canals of the air thermometer. This appears fully from the formuli© below. The theoretical introduction of the data of this apparatus is here quite simple; for it is seen that the quantity marked 8 in the equa- tion, page 212, is the one immediately given by the compensator. It will be remembered that this apparatus is essentially a porcelain stem identical with the stem of the air thermometer, iirovided, however, with a manometer tube of much smaller caliber than the tube B of the manometer, page 210. Supposing therefore that the observations are made in the way already described for constant-pressure air thermom- etry, we have at once (860) ^ 216 MEASUREMENT OF HIGH TEMPERATURES. [bi:ll.54. where rj and ti have the same signification for the compensator that Vi and Ti have for the air thermometer. Inserting the expression into the equation (5) this becomes in which the correction is evaluated experimentally. It will be shown below that the stem error is not of such serious im- I)ortance in the constant-pressure method as it was in the constant- volume method ; that the stem error rather falls below the otlier possi- ble errors of measurement. Hence the use of the compensator is not to be a« strenuously advised as it was above, and the correction derived merely from calibration and comput9*tion may be regarded satisfactory. This is, of course, a convenience, since it obviates the manipulation for the measurement of the two additional magnitudes i?i and ti, Snch statements, however, must be made with caution, for it will appear that in the constant-pressure method, inasmuch as the volume of the bulb enters fundamentally into the computation, the real object of the com- pensator is to define the volume of the bulb. The true volume of the bulb, when the compensator is used, is its own volume plus the volume of the part of the capillary tube, the length of which is the difference of length of stem and of compensator. CONSTANT-PRESSURE THERMOMETER — EXPERIMENTAL RESULTS. Man%pul 6.52 28.8 3770 6.22 O 147.8 25.6 75.12 310 6.61 2a6 3573 6.32 144.6 25.5 76.12 300 6.68 ; 1 1 28.6 3043 6.67 1 1 28.6 1 2705 6.70 1 (873) MEASUREMENT OF HIGH TEMPERATURES. Tablk el.—CoBtpariMm o. r lliermomftfr and theraio-coiipU. Seritm IT. Method of eoHHiant prrninirr. 75.M , JS.S8 ; 7i.S8 '■ TS.9sl lOXS : 2t.2 ! 2fl.I . TS.ai I a«l 3.H7 |i M.0 ' lOlKl 75. ai I SU ' 4.13 ;! ZT. t I II023 7S.Br| B50 4.38|| 27.1 ; IISTS 75.fll I »« { 4.48 I 97.6 I liHI3 75.« ; »57 1 4.J0 • 17.1 I IISW T3.W: Ka' 4.64 l' £8.2 | ll&BS 1 \ n.sn T39 S.0; ' 2e.s j uai IS.B8 «T5 1 S.I7; 2a. e diM s{ 7s.aB : 821 , S.28 ! ss.e I vasit B25 t.U II I Tables 62 to 66, exhibit tbe five oeriea of observatioos classified as Oronp 11. The last of these series (No. V) contaiij.s (>r('('liiii) bulb. The method b; which each data may be otilised ia explained below on page 236. (871) BAmm.] POHCELAIN ilB. THEBUOHETBT. 2< Tabu (S.—Compari*«» of air tlttrmometer a*d rt«rmowwiij)Ec. Strie* 1. Mttkad of w n-2M. t-is°. Vi j Ti B. I Time. Mo. • ~ !•""•■ <■. "0. cm. 1 »a *<~r». -a. I51B . SLfl 7T. 7 1 3M LIS 37 20.0 3621 L3: 15T.*; 31.7 7l 373 1.28 77. -1 379 1.38 37 20.8 J747 ■ l.B 1W.1 ■■ «.2 77. - ! 385 i.aa 37 20.8 3780 ! 1.87 JflLSl 2S.S 7 -MB 3837 ■■ 1.80 1813} 22.8 77. 7I wa i.tr? 38 21.2 3872 1 1.80 «.»' «-« 77. 3I 703 2.(2 3B 22.8 7712 ■ 1.42 ios.e ' «.* 77. 3 733 2.80 30 22.8 sua 2.18 »M.3; S5.0 3| 7« t-IH 38 23.4 WM 1.83 ti)B.a S8.0 77.1 3.23 87 24.8 8711 I.I7 108.7 ' ».B 77.1 31 762 3.90 25.1 STBS 3.00 HK.sl ^a 77. jl 703 3. S3 J7 25.8 WW 3:08 210.0 M.5 71, 4 ' 8«a 3.M 37 2<14 lOSM 3.D8 H9.2 3:.i 4I >I0 11000 . 4.13 3M.2 n.\ 4. IB 37,0 BO-sl J7,l 77. 1, ^ 4.87 3a 37.7 11088 i *.80 ?OT.5| ST.! 77. 4 031 4.«fi 38 27.0 11083 1.07 Z2J.ei 28.8 4.75 i. •■ oii 8.32 » 28.8 laiiB B.2J SM.t' 28.5 ' Ml 3(1 29.1 12113 S.40 13S.S , 28.1 Ti. I lOlD 5. AS IS 28.5 J2478 ! 8.02 223.3 1 28.7 30.2 11830 ! 0.0b 77. a DIB 8,21 37 11SS2 ' 8.17 ra,2| M.1 77.1 8^ MI2 fl-30 37 30.8 11400 0.16 2IS.I 27.7 77.1 D i M2 0.83 30,8 11057 1 0.61 8^ TTft 30,8 0201 ■ 70 77-1 30.8 esoo; 0.77 JflfcS jj'n el «5 11 m .S7 30.8 7800 0.80 !«.* 2«,K 77-1 8 1 eoa 7 08 'j7 30,8 7131 O.BB 2«.7 77. D| M7 18 37 30.7 0310 '■ 7. 13 lBiS.0 37 30.8 2S.« 77.1 S i 4B3 7 43 37 30.5 8308 T.sf. 173.2 2&t 77.1 37 30.1 8032 7.41 2&1 77.1 D i 430 7 87 37 30.1 4138 7. 73 Its. 3 28. 9> fK 37 30.0 3853 1 7.83 25.7 7T. ol 3TS - B2 37 28.8 3580 7,88 15i.7 25.7 77.1 g| 351 r 37 2S.8 3281] 808 1S0.1 25.7 77.2 sl 330 " .. „ 1. .^_ (875) 222 MEASUREMENT OF HIGH TEMPEBATURES [BULL. 6^ Tablb 63. — Comparison of air thermometer and thermo-couple. Series II, Mtthod of constant pressure. B»«ntrant balb Ko. 2. v^ = 986. t 1 = 140.7. ! No. rhermO'Ooaple Ko. t e^ oC mierovolL 37. Yi Tl cm. 1 T or. Time. ! haun. j Time. 1 ec. oe. hourt. 223.7 24.7 77.14 1021 2.18 87 ' 22.1 12654 2.22 225.4 26.2 77.14 1048 2.30 37 22.6 13095 2.38 1 227.0 25.6 77.14 1076 2.47 37 23.6 13841 2.58 227.5 25.9 77.14 1080 2.60 37 28.8 13872 2.63 224.8 26.8 77.14 1027 2.77 1 87 24.6 11692 8.82 219.8 25.7 77.14 934 2.85 ; 37 24.8 10479 2.92 214.9 25.3 77.14 868 2.95 i 87 26.1 9560 8.00 210.1 26.3 77.14 789 8.04 1 37 25.5 8793 8.08 206.2 26.3 77.14 726 8.15 37 25.8 7997 8.18 200.3 25.2 77.14 671 8.25 , 37 25.8 7326 3.28 196.0 25.1 77.13 618 * 3.38 37 26.2 6662 3.40 190.2 24.8 77.13 575 3.49 ! 37 26.4 6106 3.62 •185. 1 24.7 77.13 534 3.62 : 37 26.6 54U 3.67 180.4 24.6 77.13 409 8.73 37 26.5 5067 3.77 175.0 24.4 77.13 462 3.85 37 26.6 4643 3.90 170.0 . 23.8 77.14 433 3.97 Tablb 64. — Comparison of air thermometer and thermo-couple. Series HI, Method of constant pressure. (876) Be^nt rant bull OC. t) No. 2. «( Bo em. ,=279. 1 t=i3^. i Tl 1 ' 1 or. lermo-coup Ho le No. 39. Vi T °0. Time. Tin- ^oc-k. ec. hourt. microvolt. hourt. 223.5 23.9 76.62 989 2.58 21.4 11544 2.4H ' 4 224.9 23.8 76.62 1019 2.73 21.7 12198 2.66 4 225.5 24.0 76.62 1028 2.83 22.2 12509 2.78 4 228.7 24.1 76.62 1051 3.02 22.4 12710 2.90 . 4 227.0 24.3 76.62 1055 a 12 1 22.8 12909 3.07 4 224.8 23.8 76.60 1017 3.27 1 24.^ 11567 3.33 230.0 23.6 76.60 929 3.37 24.1 10453 3.42 214.8 28.4 76.60 846 3.47 24.2 9636 3.50 209.8 23.2 76.60 778 3.50 24.6 1 876^ 3.57 205.2 23.0 76.60 721 3.65 24.8 7454 3.75 la o 200.0 22.8 76.60 664 3.77 i 24.9 7067 3.82 195.2 22.7 76.60 616 3.87 : 25.1 6443 8.93 N 190.4 22.6 76.60 573 3.90 25.2 5020 4.05 184.8 22.4 76.60 527. 4.13 25.3 6343 4.18. 180.4 22.5 76.60 404 4.23 25.2 4977 4.28 175.1 22.5 76.60 458 4.37 25.1 4564 4.41 170.0 22.4 76. CO 426 4.48 25.1 4214 4.62 166.2 22.4 76.62 403 4.60 POBCELAIN AIB THEKHOHETBT. —Coa^mftm c/ atr ihtrmomtlm- *nd OtrnM-eompU. .Arte IV. JMkorf ^ • eetutamt pretiurt. B»«Bta ■atbnlbira.1 v. = 37>. ( = 1.^.4. ■ ITlLSf. F, T, il. t Tta». t tm Tl>». ss. M. "O. em. '0. hwn. -a. mUiTotoU. kew). 117.8 37.3 TS.DI 2.37 13027 143 t 32B.fi 37. S 7e.0l »M 3.47 2G.B 1SUB4 IN 4 37.4 MM 2.63 12133 3.i7 4 m.% 37.1 7B.01 H» 3. SB ze.o UlSB 2.B0 4 7t.01 B» J.TB 38.3 llBSfl 2.73 tSO.3 37. « 7B.W) H7 IBS 38.8 10374 3.83 7B.I10 3.» 37.0 SHO 3.BB 310. a 37.1 78.00 TI4 ' »,05 37. S B7B1 3.97 3ei.s 8se S.I5 37.4 7Bt6 3.08 in. a 17.11 7B.II0 BOB 3.S7 37.8 TWl s.3a •fi iHLa »• 78.00 sua 3.3a 3T.a 6487 S.B3 a 1M.6 MB 78.01 3.» 3S.1 Sft4S 1.48 ISt.0 W.T 78.01 m 3.C1 M.1 1503 3.ta 1W.1 »B 78.01 ut 1.7S 1B.4 8040 LN 3B.4 78.01 417 B.B7 28.4 4MS >.7t 170.8 M.3 7B.B8 iff! 3.»B 3t.4 4183 LSI Tabu 66.— CoMjiariNa tf atr OurmomtUr and tkirm»-eo¥pte. StrUt V. JMkoi ^ No. 3. ■, = 270. = 10=. r, T, * T Tine. «. tclmc «oek. tt. om. •>a Aoun. =0. Amri, 183.8 1B.B 78.2a SI 3 11.20 lfl.fl am 1L17 2.S 18.B 78. ;b S2« 11.30 1.5 1W.D 10.3 70.24 685 ILflT 17 figSt 11. SI 2.5 U-4 70,20 KB B •MO 12.07 US.8 20,1 11. B8 10 (1 nia 12.48 IB U0.0 IB. 7 78.1S MO 11. OB ■Vt IBB. a 30.4 107. B7 12.27 20 M3a 1.01 1.8 in.i 30.3 78.12 m 1.0 108.B 2L1 70. OB 734 II. M 21 BBH 1.31 1.8 HO-D 31. B 70. OB 743 12. Bi 131 «D«t l.Bl 3.0 HI. a 70. 0» 1.28 12.0 0013 3.0 7fi.>3 BU ..«, 33.8 11B80 2.90 3.7 tlt.5 38, 8 078 2.S7 33.8 11308 3.B3 3.7 34.B 3.B3 It. 8 13103 3.7 S8.3 34.3 118. M 1001 3.B7 14.B 13338 3.00 a.7 3B.1 B.17 3S.1 13388 3.33 3.T W.B 34.3 76.88 lOOfl t.37 3^4 1SU3 1.38 i:T (877) 224 MEA8UEEMENT OF HIGH TEMPERATURES. (BULL. Si. Table €6. — Comparison of air thermometer and thermo-couple, Seriet V, Method of constant pressure — Continued. Ke-eutrant balb No. 2. «« =279. « — 10°. Tbermo-conpl e No. 38. V, T, Jit ■ T Time. T eto Time, ^"f < COCK. 1 *'*'■ «r. em. °V hourt. oC. microvolt. hours. 1 1 225.0 24.3 75.54 935 3.53 25.4 12439 3.45 : ) i 219.6 23. T 75.54 852 3.64 2.'i. G 10901 3.57 ! 1 215.1 23.5 75.54 790 3.73 26.8 9803 3.66 200.6 23.3 T5. 54 722 3.84 25.8 8IJ91 3.76 205.0 23.0 7.->. 56 671 3.94 , 25.8 8126 3.86 200.0 22.7 75.56 622 4.06 25.8 7309 3.98 106.1 22.3 75.66 679 4.18 25.8 6642 4.10 100.1 22.0 75.56 .•^o 4.3f 25.6 608.'> 4.23 O ISt.O 21.6 75.57 501 4.42 , 1 26.6 5480 4. .37 179.9 2L2 75.57 467 4.53 ' 25.4 5096 4.47 175.0 21.2 75.57 436 4.Gti 25.3 4763 .4.56 170.0 21.5 75.54 405 4.78 ; ■ 25.2 25.1 4382 4134 4.68 4.77 J The results of these tables were constructM graphically by repre- senting ou the same sheet T and cwy respectively, as functions of time. For the pairs of curves thus obtained it is easy to select data for the construction of e^o as a function of T with a degree of accuracy consist- ent with the accuracy of measurement. Such data are enumerated in Tables 67 to 70, which correspond, respectively, to the four tables just described. It is perhaps well to remark that generally the interpolations are made linearly. This involves less assumption and less work than other £:raphic methods, and the i>oints are sufQclently near together to make it available. Tables 67 to 70 correspond to the data of Group I, Tables 5S to 61, Table 67. — Corresponding to Table 56, Series I.— Re-entrant bulb No. 1. ! No. «M ■'! No. 010 37 37 87 37 37 370 3630 ' 37 780 8950 300 1 3810 87 800 1 0200 400 3910 37 820 9470 410 1 4050 i 87 840 , 9770 420 i 4170 •' 37 850 9940 37 860 > 10100 (878) "fc BABUS.] PORCELAIN AIR THERMOMETRY. 225 Tablb 68. — Correapondwg to Table 59. T Series 11. — Ke-entrant bulb No.l. No. 1 6520 i No. T 824 eio No. T *!• 37 610 1 37 9740 J ^ 600 6430 37 640 7160 37 920 11200 37 550 5820 37 667 7700 ! 37 930 11300 37 500 5220 37 720 8290 37 933 11330 1 37 450 4640 37 727 6270 37 750 85K0 i 37 400 4030 87 800 9410 1 37 TOO 7820 ; 37 350 3420 37 820 96C0 ' 37 1 G50 7100 1 37 300 2800 Tablk 69.—Corr€8i)onding to Table ()0. Sorien III.- • -Re-entrant bnlb No. 1. , No. T eto No. T en No. 1 T CM 37 330 3120 37 860 10200 1 ! 37 800 9320 37 3G0 3500 37 880 10500 1 37 750 8640. 1 37 425 -1300 37 900 10800 37 700 7960 37 440 44GO •[ 37 920 11150 1 87 650 7250 37 453 4600 'l 37 060 11850 37 600 6550 37 630 7100 i 37 980 12170 37 5.'i0 5880 37 060 7500 |. 37 990 12340 j 37 500 5280 37 690 7860 ' 37 994 12370 1 37 450 4700 37 710 81G0 ! 37 950 11580 37 400 4080 37 718 8270 37 900 10760 i 37 350 3420 87 840 084U 1 37 1 850 10040 ; 3' 300 2840 Tabi.k 70. — Corresponding to Table i)l. 330 3.y) I 370 I 390 ; 480 ' 500 I 520 540 640 660 680 Series IV. -Re-entrant bulb No. 1. No. 37 37 37 87 37 37 37 37 37 37 37 1 No. r 1 3010 i 37 1 700 ; 3330 . 37 770 3620 37 790 3850 ! 37 810 4960 37 815 5220 37 870 5470 i 37 890 5740 37 910 i 7200 1 37 , 030 , 7430 37 950 7680 37 957 evt 8050 9000 9280 95r)0 9650 10520 10860 i| 11170 11470 11700 11800 850 I 800 I 750 700 650 600 I 550 I 500 j 450 I 400 I 350 ' 10320 9470 8670 7970 7340 6660 5970 5280 4650 4020 3430 The series of Tables 71 to 75 correspond to the iLita of Group II, Tables 62 to 66. (879) Bnll. 54 15 226 MEASUREMENT OF HIGH TEMPERATUKES. [BULL. 54. Table 71. — Corresponding to Table 62, Series I • No. eM T No. mierovolt T No. eM T mierovolt^ oa oC. microvolt. OC. 87 3410 359 37 10040 895 37 842 37 3570 873 37 10850 910 37 8900 779 37 3700 379 ' 37 11080 928 57 8160 724 37 3770 385 30 11090 938 37 7450 G65 39 3850 893 1 39 11070 931 37 6380 606 39 3900 396 30 11050 927 37 6080 5fi7 39 7970 703 39 12120 972 37 5r>90 529 39 8340 733 39 12290 991 37 5060 493 : 39 8470 744 39 12440 1019 1 o^ 04 4730 460 87 8070 758 37 11720 9C3 37 4330 430 1 37 8800 762 37 11470 949 37 3040 402 87 8800 763 37 11400 952 37 37 3660 3370 375 351 i 37 330 Table 72. — Corresponding to Tables CJJ, G4, 65. Series II. 1 ~ ■" No. Series III en microvolt. i T Series IV « No. mierovolt. r No. mierovolt. T oc. ! °0. 87 12650 1030 39 11900 989 37 12040 986 37 12870 1048 39 12370 1019 37 12060 990 37 13250 1076 , 39 12590 1028 1 37 12110 990 37 133G0 1060 zy 12850 1051 37 12140 995 37 11250 034 1 39 12910 1054 37 11120 920 37 10150 858 1 39 11670 965 1 37 10040 847 37 9170 789 39 11080 920 ! 37 8970 773 37 8240 726 39 39 9880 846 37 8110 714 37 7540 671 8880 778 37 7410 659 87 6780 618 1 39 8180 721 1 37 6740 609 37 6250 575 39 7330 664 ; 37 6180 5G9 37 5660 534 39 6780 616 i 37 5640 531 37 5220 499 39 6170 573 37 5U0 490 37 4820 462 39 5550 527 j 37 4740 459 37 433 39 ' 39 5150 4700 494 ! 458 37 37 4350 4140 427 413 39 4350 426 i i 1 "^ 403 1 (880) , ^ i ■ ty r i t : UARUB.] PORCELAIN AIR THERMOMETRY, 227 Table 75.— Corresponding to Table 66. Series V 1 No. eto ! T No. en mieroitoU. T No. eso T microvoU. °a oa' microvoU, OO. 38 5370 512 38 9030 774 38 7580 671 38 5560 526 38 11700 958 38 6860 622 38 5900 565 38 11950 978 38 6300 579 38 5030 568 j 38 12300 1002 38 5740 539 38 6030 560 38 12430 1006 88 5290 501 38 6100 667 38 11470 935 38 4880 467 38 8310 734 38 10130 852 38 4450 436 38 8500 742 38 9190 790 38 4100 405 38 8850 760 38 8270 722 Graphic digesU. — The results of these four tables may be platted graphically by making e^ a function of T. This is done in Figs. 41 and 42, which may be said to be the final result of the calibration problem in hand. Fig. 41 contains the data of Group I, Fig. 42 the data of Group II. In Fig. 41 numerals inserted show the series to which the point of observation refers. If temperature be increasing (heating) the numeral is placed above the point; if temperature be decreasing (cooling) the numeral is below the point. In Fig. 42 similar distinctions are carried out by caudal dashes. For increasing temperature these i)oint upward or to the right; for decreasing temperature downward or to the left. CONSTANT-PRESSURE THERMOMETER — DISCUSSION. Errors of measurement in general, — The discussion of the data, Tables 67 to 75, may expediently be introduced by an analysis of the effect of errors. The divers quantities, whicli enter saliently into the equation, derived for constant-pressure air thermometry, are here ty Ti Vi v^ V V H , to which may be added M and S, As above, the degree of absolute ac- curacy witli which they are to be measured in order that the effect on « T may not exceed 1 : 1000, follows from the equation dx=^ dx T_ dT 1000 where x typifies any one of the quantities enumerated. From this fol- low the subjoined special equations, all of which are ai)proximate, and put in such forms as will best facilitate the computiition : 6M=:^ a T 1000 (1+«T) 2 (881) i \ 228 MBASL'RKMENT OK HIGH TEMPKUATUUES. |bull.S4, °^~ 1000 (i + «r)* a °^ «Zi « ^ _ 1 ^v " V ~1000/{2'i) (l+«T)*-~/(2',)° r' a T 1 '^¥^ioo(r[/(i»)— /•(t'ijXi+«r)'=~[/(p^)— /(OJ*^'^ «»» r »' 08cs t and Ti may be supposed identical. (882) • n // " 99 ff 39. ,1 ,, M. " V 99 99 ,«> n /tr " 99 fP 37. S » y " f9 99 30, iOOO Zo^ 7B5' 900* 900* Fio. 42.— Chart showing the variation of therm o-electromotiye force (microrolts) with temperature. BARV8.J PORCELAIN AIR THERMOMETRY. 229 6{H/h) must be dorived from the general equatiou, wbich, after diflfer- entiatioD, is simplified by inserting H=zh, If into these equations we introduce mean values, such as #=20^, y Ti=20o, a=0.00367, /5=0.000017 ; if, moreover, we insert for — ^ the values which may be taken from Tables 58 to 66, above, then the said equations lead to the following tabular comparison. It is expedient in addition to the absolute values of the divers errors dt^ dT^, dVi, Sv'y dv, da, d/3j 611, dilf, dS, which individually influence the result by 1 : 1000, to give also the relative values of some of these quantities, or again the error of the ratios, viz : T' K^y \^')' K^y <^(^/-'''»'^^<^(«)/'»- Tadle 76. — Comparison of divers errors tchich affect the result one pro mille. 6t 100 500 1000 1500 0.06 0.07 0.05 04 5r, —0.29 —0.12 —0.07 —0.05 ce. 0.059 iv* ee. —0.632 0.009 ! -0.155 0.051 I —0.081 0.039 i —0.056 6v «^/^ ec. — 0. 276 0.17 —0.111 0.08 —0.060 0.05 —0.047 0.04 V r / r, r ylO* 211 245 180 140 xlO^ —2.26 —0.50 — 29 —0. JO 6M/2I xlO« —268 — G47 —736 —846 «^xlO« 6U 1 lJj/xlO» 68xl(fi ein. 2.7 0.016 —197 197 1.3 0.019 —228 228 0.8 0.014 —168 168 0.6 O.Oll —130 130 -. -— -■ - -. — =r _ - - . -- ^ - — -—l: — ij. — 6ii!S xlO* Vt 1 . ce. o(7. —5.27 211 59.9 100 —1.30 245 173.0 500 — 0.C8 183 215.3 1000 -0.40 141 233.6 1500 From this table of errors a fully satisfactory inference of the value of the experiments made can be obtained. 6 M and osition of the series of points marked "I'' is easily accounted for. Nor was a correction aj)- plied in these cases for permanent variation of the volume Vq. Again, in Series II an accident by which the thermo-couple was withdrawn from the air-thermometer bulb cooled the electrical apparatus abnor- mally. This occurred during the stage of decreasing temperature, and the lateral position of certain points marked ^^2^ on the diagram is also accounted for. The remaining points are grouped in close proximity to a uniform locus. The maximum elongation of any of the points, 2, 3, 4, in question is not greater than 10^, whereas, as a rule, this differ- ence is very much smaller. At the outset it is to be borne in mind tljat into this aggregate maximum discrepancy of 10^ are crowded all the errors of the thermo-electric measurement, to say nothing of the errors incurred by the double graphic interpolation by which Fig. 41 was derived from the individual time series of observations of e and T. Of course, results of this kind are susceptible to great improvement if the observations are made by a number of observers instead of by one ob- server only, for in this way the time error may be eliminated, and observations may be made simultaneously. Quite apart from these considerations an error of 10^ is easily incident to the method in its present stage of experimental development. However carefully the manometer may be screened from the furnace an error in T^ of 0.2^ C, or even more, is not improbable; nor was the attempt made to measure Fi with greater precision than O.V^. This already accounts for half of (885) 232 MEASUREMENT OF HIGH TEMPERATURES. [bull. 64. « the observed maximum error, apportioning the remaining four or five degrees to the variety of discrepancies already enumerated, to which may be further added changes both of v, the capacity of the bulb, and of /?, due to vitrification or similar progressive change of the substance of the porcelain during successive heatings; to irregular differences of the stem error; to the possible occurrence of minute capillary leakage throughout the considerable length of connecting tube; to structural changes (crystallization, silicification, gaseous corrosion) of the metal of the thermo-couple. It is needless to make further mention. Considering the figures 41 and 42 as a whole, it will be seen that the calibration curves are regular throughout In case of the 20 per cent, platinum-iridium alloy, therefore, no evidence of sudden allotropio changes or polymerization is anywhere discernable. Hence between 300° and l,300o, the availability of the given platlnumiridium alloy for thermo-electric pyrometry can not be disputed. I do not believe that the strictures which Le Chatolier (I. c.) has placed on the pyrometric use of the platinumiridium alloys are substantiated by experiment, though they may be true (Chap. 1) for low percentiige alloys. A full discussion of the divergence of the said curves (Figs. 41, 42) from the Avenarius- Tait equation, is beyond my present purpose. Accuracy of the measurements made^ Oroup II. — In a general way these critical remarks apply to the data obtained with Bulb II and in- serted in the chart (Fig. 42). The method of designation is clear, the divers series being distinguished on the chart by dashes, which pass upward or to the right for ascending tenii>eratures, and pass downward or to the left for descending temperatures. As a whole, the data for Bulb II are a marked improvement upon the data for Bulb I. This was brought about principally by correcting the calibrated volumeof the bulb by such permanent changes of volume as occur after each he^iting. For- tunately the value of this correction can be found with great accuracy and facility by the same method by which the fiducial temperature is determined (cf. page 213). If dv be the permanent alteration of the vol- ume of the bulb due to heating; if h^ and f^ be the pressure and tem- perature before heating, and \ and t^ the pressure and temperature after heating, for which, in each case, the air is wholly in the bulb and capillary stems (i. 6., Fi=0); and if 2{v) be the total original volume of bulb and capillary stems, then hj{t,) -hj{t:) _ 8v^ Kf{ta) 2v' The quantity bf{t) occurring in this equation is the same already evaK uated in equation 6 (page 213). The following tabular exhibit of the values of dt? in question was obtained from Bulb II. "% (886) UABUS.J PORCELAIN AIR THERMOMETRY. 23S Table 77. — Permanent volume variations of hull. ¥(t) vo ec. 381.26 279.10 279.30 279.22 279.33 279.30 Mean volumes Vo Before Series I After Series I After Series II After Series III After Series IV After Series V 72.677 73.240 73.188 73. 210 73.180 73.188 +6.98 -0.71 ±0.00 -0.30 +0.11 ±0.00 ee. I 280.18 I 279.20 I 279.26 1 279.27 j 279.32 The values of t'o in the last column are therefore the closest approach to the respective zero volumes of the bulb during the successive series I to V in question. It is this corrective which makes the results' of Fig. 42 very much more uniform than those of Fig. 41. If Fig. 41 be compared with Fig. 42 it will be seen that the agree- ment of loci is very good. It is clear, beyond question, that the discrep- ancies involved are those incidental to the measurement; discrepancies, moreover, which are capable of considerable reduction by improving the experimental appurtenances in the way suggested above. It therefore follows that the degree of identity of the environment of the air thermom- eter and of the thermo coui)le is as nearly perfect as the calibratioti problem demands. Again, from the difficulty I have found in obtain- ing accordance between diU'erent series of results in the earlier experi. roents, I believe that with the use of the present form of re entrant bulb the calibration problem has for the first time been rigorously solved ; for it is obvious that if the constants of either of the loci (Figs. 41 or 42) were calculated by the method of least squares their probable error would be decidedly within one pro mille. Boiling point of zinc, — This is the stage of progress at which my other duties will make it necessary to temporarily abandon the temperature problems and proceed toward a corresponding development of the press- ure work. I need merely notice therefore in what respects the ab- solute data of this chapter substantiate the earlier inferences. For instance, if the values of 6207 which hold for the boiling point of zinc given at the end of Chapter II, be interpreted by aid of the final dia- »A curious source of error may be noted here. When the centrifugal blower is in- sulated the friction of the belt electrifies it permanently. If, furthermore, the tubing be insolated the furnace will be charged with a current of elcctrifled air. Through the wires of the thermo-couple this charge is distributed over the measuring appara- tus. If now, any metallic part of this (for instance, the metal of a rheostat key) be touched with the linger there results a redistribution of the charge aud invariably a large deflection of the galvanometer needle. This is seriously misleading, and the error is not always at once detected. Care should therefore always be taken that the tube oonveying air to the furnace from the blower is not insulated. (887) 234 MEASUREMENT OP HIGH TEMPER ATtlRES [bvlu5L grams (Figs. 41 and 42) the data so obtained are small, being not larger than 905^ in the one case and 916^ in the other. These valaes are to be finally corrected by the valne for t?o, found after the completion of the measarements by direct water calibration. I may remark in pass- ing, that the stem correction is negative, and that I applied a value which is certainly not too large. Hence the stem error has produced no*erroneous negative increment of the value of T. In the case of Bulb I, the datum Vo is accepted as 280^<^, an approxi- mate value to be subsequently corrected for permanent changes of vol- ume, etc. By the volumetric method (page 214) the volume of bulb, stem, and capillary tubes is found to be 280.73*^^ at the mean temperature 2(K>. From this is to be deducted the volume of the metallic capillary stems, 0.40**®; the volume of the porcelain capillary stem, 0.53*'*'; and the amount of dead space at the joints of the .tubes, 0.23*'*'. This leaves for the volume of the bulb at OOC. ro=279.58<'^ GThe same volume was meaaured at the close of the work by direct cali- bration with water, and found to be ro=279.06*'^ This diflference of 0.62*'*' is due to the imperfection of the volumetric method in its present form. Preferring the latter value, the volume in- crement for Bulb I is I II IV vj o 012 000 025 o 916 o 1 909.0 ' 918.8 4 91« 024 915 914 Hence, if to these mean valaes be added the corrections ST as jast found, there follows T=921.5o for Bulb I and T=926.4o for Bulb II. A final correction is still to be added. In the present reduction I assume 620=11,000 as the electrical equivalent of the boiling point of zinc. The careful crucible exi)eriments made soon after the air ther- mometry, and detailed on page 123, show that ^=11,074. Hence, since ST =z de2o/{a + 2bT) nearly, and since 6 ^20=+ 74, it follows that ST = 4.70. The constants a and b are calculated from the data of diagram (Fig. 42), a sufficient approximation. Hence, finally, T=926o for Bulb I, and T=931o for Bulb IL This is the closest approximation to the boiling point of zinc which the method, in its present stage of development, permits. This is a low result as compared with Deville and Troost's, and with Weinhold's data. It agrees admirably with the values of Becquerel and of Violle. But my datum is not as low as would have been anticipated from the constant- volume measurement^^ (page 199) of this chapter, or from inferences deduced by purely thermo-electric measurement in Chapter II. As long, however, as rigorous measurement of the vari- able /?, the coefficient of expansion of the bulb, has not been made, and the effect of a non-glazed interior of the bulb has not been placed beyond all obscurity, it is wise to advert to the present value for the lH)iling point of zinc with only precautionary emphasis. Nevertheless, it is pleasant to note this accordance of data between the results of the French observers mentioned and my own data. I am specially encour- (889) 236 MEASUREMENT OP HIGH TEMPERATURES. [BULL. 5i. aged in believiDg the nou-inglazed thermometer bulb nearly as avail- able and safe for high temperature measurement as the inglazed form. Coefficient of heat expansion of porcelain, — It is necessary to state that iu the present work no special measurements for /3 have as yet been made. The value taken is that of Deville and Troost, which, for the porcelain in hand, is possibly too low. The probable effect of cor- recting /^ will therefore be an increase of T, since increments of both /a and T have like signs. Not wishing at present to redetermine fl I made corroborative tests in the following manner : In Table 66 results are given from which approximate values of the coefficient of expansion of porcelain may be computed. Let the ma- nometer volume be changed when the temperature of the bulb is nearly constant. Then if JBT,, Fi, Ti,andfl2, V^, T, are two successive readings, it follows that JhV V « ^r,) -"■/'/( r.) B 1—112 where T is the temperature and v the zero volume of the bulb. It is expedient to make Hz the barometric height for the day, so the T can at once be computed by the ordinary formula. /3 may then be com- puted for/(T). By making the measurements for T {i. e., Hi, Fi, Ti) alternate with the measurements for /^ (i. e., Hz, F2, T2) in time series, the value of T, which corresponds to the time at which the measurements for /3 are made, may be accurately determined by graphic interpolation. The following results are computed from the data already given in Table 66, Bulbil, Series V: Tablk 79. — Coefficient of heat expansion of porcelain. Tiuie. A. f/i. 11 45 T fi 568 11 53 12 03 (5C4) 560 I 0. 000022 12 U(I 12 25 (564) 567 I 0.000026 2 34 978 2 50 2 58 (993) 1002 I 0.000037 3 10 3 16 1(^04 1006 5 0. 000027 • ^< In view of the fact that the (]uantities on which /3 ultimately dei)ends of the same order of magnitude as the stem error J^, this method determining fi can not be looked to for verj' close results. Indeed, if (800) BABU8.1 PORCELAIN AIR THERMOMETRY. 237 p were known from special measureraents this valne could be used to compute '2. It is obvious therefore that for sharp values of /? it is necessary to work with a jacketed manometer, so that Tx may be con- stant. It is necessary also that T and H be constant, a condition which the above experiments do not quite fulfill. The above data, crude as they are, show, however, that fi is determinable by this method with the same degree of accuracy with which it is to be applied. In this respect the constant-pressure method is unique^ since it admits ofea^y modifications by which the zero volume of the bulh, its coefficient of expansion, as well as all permanent changes of volume, may he evaluated without extra appliances. [Attention may again be directed to the independent method of standard- ization of a noninglazed reentrant porcelain air-thermometer bulb by thermal comparison with a re-entrant glass thermometer bulb of known constants. Such comparison is to be made above 30(P to obviate the moisture and condensation errors, and either directly in the elliptic re- volving mufSe (Fig, 36 a), or indirectly through the intervention of the same thermocouple. In the last case each bulb is separately compared with the couple as explained above (Figs. 37, 38), and the results then CO ordinated. The hard-glass bulb, according to Troost (loc. cit.) may be safely regarded rigid as far as COOo. 3889.] Remarks, — The manner of further development of the present ther- mal problems is now sufficiently obvious, and may be briefly summar- ized in a final remark. It is necessary in the first place to ngorpusly compare bulbs glazed interiorly with bulbs not glazed interiorly. The latter are so much more easily constructed that if their use be warranted practical air thermometry will b§ in no small measure facilitated. For instance, if we suppose the bulb non-glazed interiorly to be admissible, then there are no serious obstacles in the way of a fire-clay thermometer bulb. Bulbs of such ware are naturally porous, but there is no doubt that enamel can be applied in sufficient quantity to the exterior to make them impervious to air. With these bulbs the upper limit of possible thermal measurement will closely approach the melting point of pla- tinum. By aid of the volumetric method described on pages 195 and 214, problems referring to the internal volume of the bulbs and stems, whether porous or not, admit of satisfactory solution. Again, it is nec- essary to compare the data of bulbs containing different gases, dry air, O2, 112^1^2, etc. All such comparisons can be made either directly, by exposing the bulbs contiguously in an elliptic revolving muffle of the kind sketched and described on pp. 182, 188, or they may be made indi- rectly, by comparing the individual air-thermometer bulbs with the same thermo-couple. In the interest of greater accuracy the same re-entrant form of bulb, into which the divers gases are successively introduced, is expediently combined with one and the same thermocouple, and the heating is conducted precisely in the manner shown in this chapter. Until Charles's law has in this way been tested for large rangesof tem- perature it is hardly desirable to multiply the number of approximate (891) 238 MEASUREMENT OF HIGH TEMPERATURES. Ibull.54. thermal data in tbe region of high temperatares by farther data of an absolate kind, which at the present state of our knowledge most also be regarded as approximate. The first steps of a method by which rigorously accurate data may be reached the present chapter ftdly elucidates. * For pur];)oses of ordinary high- temperature measurement the con- stant-pressure method of air thermometry must undoubtedly be pre- ferred. It is superfluous to reiterate the many reasons which the text contains. But for the ulterior and purely scientific purposes of study- ing laws relative to the expansion of gases at high temperatures, both methods are equally valuable, and it is highly probable that an investi- gation of the thermal-expansion phenomena of one and the same gas in all admissible states of tenuity will throw more light on the subject in hand than an inquiry into the analogous behavior of different gases. Fortunately, in ail such comparisons the stem errors so nearly counter- balance each other as to make it probable that the measurements can be made with great nicety. (892) \ CHAPTBE V. THE PYROMETRIC USE OF THE PRINCIPLE OF VISCOSITY. INTRODUCTION. Remarks. — It has been said that a method for making metallic capil- lary tubes was described hypothetically by Begnault in his celebrated memoir.* So far as I know, however, the first platinum tubes made for actual high-temperature use are those described in the present volume. The dimensions oC the capillaries used in the air-thermometer work have already been given; similar tubes of silver and of copper were also in hand. It seemed expedient therefore in view of the excellent quality which these tubes eventually came to possess, to put them to more general use than originally contemplated. Indeed, the attempt to obtain absolute thermal measurements in the region of high temper- atures, from the transpiration data obtainable by passing gases through ledhot capillary tubes of platinum, presented itself as an important linal step in the present investigation. The kinetic theory of gases has not, as yet, given any satisfactory clue for the prediction of the thermal relations of gaseous viscosity. It is nevertheless probable, from the nature of a gas, that an experimental law, which might be found to hold between 0^ and l,200o, could be safely assumed to hold for a much larger interval of temperature. In other words, judicious extrapolation is much more nearly permissible in the case of thermal results applying to gases than it possibly can be in the case of results which apply to liquids or to solids. Again, since the rate at which transpiration takes place varies inversely as the absolute temperature of the gas, as well as inversely as its viscosity, it is clear that the construction of a trans- piration pyrometer will be practicable, even if the thermal variations of viscosity should prove unfavorable for such a purpose. Apart from practical applications, however, physical science can not but profit by any attempt at high-temperature measurement, rationally based on some other phenomenon than the thermal expansion of a gas. This is proven, for instance, by the pains which V. Meyer, Troost, Ber- thelot, and others have taken to ascertain whether the coefficient of thermal expansion in all its high-temperature applications could be as- sumed to be rigorously constant. Even if the present method should fail of further purpose than the co-ordination of data in a field of high temperature, where absolute results are either isolated or wanting, its ' Cf. pages 167, 169. (893) 239 240 mi:a81jrkment of high temperatures. rBULL.54. coiiditious of application deserve most careful scrutiny. I am justified in believing that the favorable character of the results which this chap- ter contains will be sufficient to show that the transpiration pyrometer is more than equal to the demands made upon it. Interpreted by the Poiseuille-Meyer formula transpiration data must enable us to measure temperature absolutely, over a wider thermal range, and with greater convenience and accuracy than is now possible with any other instru- ment. An important part of the present chapter is the new light it throws on the thermal relations of viscosity and on the thermal relations of the mean free path of the molecule of a perfect gas. The phenomena of diffusion, heat conductivity, and viscosity in gases, depending, as they do, in their thermal relations on the law of force between the molecules, have hitherto remained beyond the reach even of theory. The i)resent chapter is divided into two parts, the first of which con- tains experiments made with true capillaries. The SQCond part contains experiments with tubes of larger bore — with tubes, in other words, which do not strictly satisfy the capillary conditions of the Poiseuille- Meyer law. Literature. — The work of the earlier observers has recently been discussed with great thoroughness by Mr. S. W. Holman^ in the last of his fine treatises on the relation of viscosity of gases and tempera- ture. Profiting by this, I will therefore dismiss the subject with a few cursory remarks, and refer those desiring more specific information to Mr. Holman's researches. Historical reference is also made in O. E. Meyer's* extended article, where the salient features of Graham V classic experiments are analyzed. A clear account of the whole question is given by Meyer in his well-known book.* Some years after Graham had published his experimental results, and after Clausius* had pointed out the kinetic importance of the mean free path traversed by the gaseous molecule, the questions relating to the viscosity of gases were placed on a new theoretical footing by the remarkable results of Maxwell.^ Using StokesV results to treat the viscosity of air, Maxwell is able to express the mean free path of the molecule absolutely. The data here in question were derived by Cou- ^ » S. W. Holman : Proc. Am. Acad. Arts and Sci., vol. 21, 1886, p. 1 ; Phil. Ma^., Lon- don (r>), vol. 21, 188G, p. 199. «0. E. Meyer: Fogg. Ann., vol. 127, 18(56. pp. 253, 353. 3 Graham: Philos. Traus. Roy. Soc., London, 1846, p. 573; ibid, 1849, p. 349; Ann. der Chem. uud Phann., vol. 76, 1850, p. 138. * Die kinetische Theorie der Gam^ Breslaa, 1877, p. 123. •^Claiisins: Pogg. Ann., 4th series, vol. 15, 1858, p. 239. <* Maxwell: Rei>t. 295111 Meeting Brit. Assoc., 1859 (1860), notices, etc., p. 9; Phil. Mag. (4), vol. 19, 1850, p. 19. Less closely allied resalts in Phil. Mag. (4), vol. 20, 1860, p. 21. ^Stokes: Trans. Cambridge Philos. Soc, vol. 9, 1850, p. 166 ; ibid., vol. 10,1851, p. 105. Fortschr der Physik, 1850 : 50 ; p. 101 ; Pbil. mag. (4) I, 1851, p. 337, (894) BARUB.1 VISCOSITY OP GASES. 241 louib's method of vibrating plates, a method which does not serve well for the determination of the thermal relations of mean free path, although it has been api)lied with this end more or less fully in view by Meyer,^ by Maxwell^ himself, by Puluj,^ and others. Among these observers only Puluj, nsing an apparatus devised by Kundt and Warburg, suc- ceeded in deriving good results. Very important service was therefore done to this branch of molecular kinetics b}^ the elaborate researches of O. E. Meyer.* Availing himself of the general differential equations for the motion of a viscous fluid published by Stokes,* or those more recently published by Stefan,^ O. E. Meyer deduces the well-known equation, in which the rat^e of transpiration is fully expressed in terms of the terminal pressures, the viscosity of the ga«, the coeflftcient of external friction, and of the dimensions of the capillary tube through which the gaseous flow takes place. Calculating from this result the volume of gas transpiring during a given time, under given conditions, Meyer reaches a result which, for gases, is the complete analogue of the law for liquids experimentally deduced by Poiseuille^ and flagen,* and to which Stokes^ and others (Neumann, Wiedemann, Hagenbach, Ste- fan, Helmholtz) have given a theoretical foundation. It is by using this equation that Meyer^^ himself, discussing Grah«*m'8 results, in later work,^^ l>artly in conjunction with SpringraUhl,^^ derived the first good results for. the thermal coefficient of viscosity. Such results have since been obtained in greater number and with greater elegance m transpi- ration experiments, made by Puliij,^^ v. Obermayer,^* E. Wiedemann,^^ Warburg,*® Schumann,*" and particularly by Ilolman,*^ to whose elegant and elaborate researches I have already referred. In all of these cases, however, the data in hand are essentially low- temperature results. The largest range of temperatures occurs in Obermayer's later research, in which the thermal relations of the vis- » O. E. Meyer : Pogg. Ann., vol. 125, 1865, p. 177 ; 51h series, vol. 23, 1871, p. 14. 2 Maxwell : Pbil. Trans., 18(56 (I), p. 249. aPuluj: Wien. Sitzaugsber., vol. 73 (2), 1876, p. 589. * O. E. Meyer: Pogg. Ann., vol. 127, 1866, pp. 253,:jr»3. '^Stokes: Trans. Cambridge Philos. Soc., vol.8, 1847, p. 287. «St.efan: Wien. Ber., vol. 46 (2), 1862, p. 8. ^.Poiseuillo: M^ni. Sav. £trang., vol. 9, 1846. p. 4:i3; Ann. cb. et phys. (3), vol, 7, 1843, p. 50. « Hagen : Abb. d. Berl. Akad., 1854, p. 17. ^Stckes: Trans. Cambridge Pbilos. Soc, vol.8, 1847, p. 287. »oMeyer: Pogg. Ann., vol. 127, 1866, p. 367. »i Meyer: Pogg. Ann., vol. 148, 1873, p. 1 ; ibid., p. 203. »* Meyer u. Springmiibl: ibid., p. 503. "Pulnj : Wiener Sitzungsber., vol. 69, p. 287 ; vol. 70, p. 243, 1874. ^*y. Obermayer: Wiener Sitzungsber., vol. 71, 1875, p. 281 ; vol. 73, 1876, p. 433. i» E. Wiedemann : Fortscbr. d. Physik, vol. 32, 1876, p. 206. »6 Warburg: Pogg. Ann., vol. 159, 1876, p. 403. "O. Schumann: Wied. Ann., vol.23, 1884, p. 3.53. ^^ ^o]mau : Proc. Ann. Acad. Arts and Sci., vol. 12, 1876, p. 41 ; ibid., vol. 21, 1886, p. X. Bull. 54 16 (895) / 242 MEASUREMENT OF HIGH TEMPERATURES. Iwi;ll.54. cosity of a number of gases are studied between — 21^ and 280o. Mr. Holman's later researches go as far as 224^ for CO3 and 1249 for air. E. Wiedemann observed in thermal baths of steam (100o> and aniline vapor (I850). Hence, if the transpiration data are eventually to sub- serve the purposes of temperature measurement, it is necessary in the first place to investigate the law of variation of viscosity and temi>era- ture for a range of variation extending above 300^ as far as possible into the region of white heat. Since this law is necessarily a fundamental consideration it will be in- expedient to report my work in the chronological order of development. It will be preferable, first, to give such results aa have an immediate bearing on the law in question, and then to extend the work by an investigation of the flow of gases through tubes to which the term "capillary," taken in the sense of the conditions under which Meyer's formula holds, does not strictly apply. For very short tubes Navier* investigated the theory of efflux ; for very long tubes these conditions are equally well known from the stated investigations of Poiseuille and Meyer, For tubes of intermediate dimensions, however, the informa< tion in hand is comparatively meager, although recent investigations of a relevant character have been published by Osborne Eeynolds,* by Guthrie,^ and by Hoffmann.* TRANSPIRATION SUBJECT TO THE POISE UILLE-METEM LAW. APPARATUS. Oeneral disposition of parts, — The great degree of perfection which Professor Eichards^ has attained in his jet aspirators suggests the use of this apparatus in the present experiments in a manner similar to that employed by Holman. Such adjustment was at first contemplated. Keasons, however, into which I need not enter here, together with the fact that in some of the experiments larger pressures were demanded than those which the jet pump could furnish in our laboratory, led to the employment of absolute methods and of the special apparatus now to be described. It consists essentially of two large vessels, one placed as far as may be necessary above the other and connected by wrapped rubber tubing. The upper of these vessels is filled with mercury and the lower contains the dry air to be forced through the train of capil- lary tubes in connection with it. In this way a column of mercury of any desired height is brought to bear on the lower vessel, and the.de. tails of adjustment are then to be such that this pressure may remain constant throughout the course of the experiment. '- Navier: M6m. Acad. Roy. des Sc, vol. 9, 1830, p. 336. 2 0. Roynolds: Roy. Inst. Gr. Brit., 1884. p. 1; Boibliitter, vol. 10, 1886, p. 217. 3 Guthrie: Phil. Mag., 5th ser., vol. 5, 1878, p. 433. *Hoflfniann: Anu. der Physik, Wicdoniaon, new series, vol. 21, 1684, p. 470. ^Richards: Am. Jour. Sci., 3d series, vol. 8, p. 412; Trans. Am. Inst. Mining £ngi- ^ neers, vol. 6, 1879, p. 492. Mb (396) VISCOSITY OF GASEB. In Fig. 43 the apparatns for pro- ducing tlie pressnre in qaestioii is fully giveu. The scaSbldiiig consista of fonr vertical tiil>es of gna pipe, ab, ab, ab, ab, about IS*™ apart and 200"" high. They are screwed helow to a suitable base and coupled together above, forming together a long rect- angular cotamn of square section. The tops of each tube eud in vertical and lateral sorews a, a, a, a, to which similar pipe may be attached, either vertically or horizon tally, thusgreatly increasing the efficiency of the stand- ard either for the present purposes o: for use iu supporting the manome- ter tubes of an air thermometer (cf., pp. 168, 209). The two vessels for tuer- cury are shown at ^1 and B, of which B is stationary, while A can be raised to any necessary height by the cord FOB passing over the pulley Q uud fastened 1)y a fiat-headed thumb- screw, H. The vessel A is practically a Mariotte dask, provided with a stop-cock at C. B has a similar stop- cock at D, and the connecting rnbber hose is shown at (JED. These con- nections, in addition to the stopcocks C and i>, should be of wide twre. so as to insure a nearly frictiouless flow of mercury. The head of the vessel B commu- nicates with the capillary tube /, carries the open mercury manometer R for the nieasnremeut of presanres, and is iu connectiou with a stop-cock (not shown in figure), by means of which atmospheric air or any other gas may be introduced into B through a desicating tube. As this will be more clearly shown iu the diagram below, I need only say that the cap- illary tubes are shut off by a faucet, K. Finally, a wide lateral tube, P $, ID commuuicatioQ with the (89J) \ 244 MEASUREMENT OP HIGH TEMPERATURES. [bull. 54. rubber bose at P, enables the observer to let the mercury flow into the receiver B from above by closing the stop-cock D. As this is the special feature of the present apparatus, and is essential for the maintenance of constant pressure, I will describe it further. Suppose the Mariotte flask A to be hoisted in and fixed in the high position ; suppose' the receiver B filled with air, and communication with the atmosphere and with the capillary tubes to be shut oft', moreover, the stop cocks C and 1) closed. If now G be opened, mercury will flow from Aio B through the hose and the lateral tube P Q, The head of mercury urging the influx will be the difl^erence in height between Q (the point of influx) and the lower end of the tube c? in the Mariotte flask A. The flow will continue until the manometer R registers the equivalent pressure. If, now, the stop-cock K of the capillaries be opened, the air from B will be very slowly discharged into the atmos- phere and the mercury from A will slowly flow into the receiver By en- tering it from above in such a way that the pressure is maintained con- stant throughout the course of the experiment ; for tfie head of mer- cury between Q and the Mariotte level remains unchanged until B is quite filled, and the pressure value of the head is read oft* on the ma- nometer B. Special care, however, must be taken with the construc- tion of the Mariotte flask; for inasmuch as the flow from such a flask is necessarily intermittent, the period of intermittence mus| be reduced to the smallest possible amount by compelling the air to enter A through d in very small bubbles. The h)wer end of the tube d is there* fore drawn out into a capillary of, say, 0.05'^'" diameter, which is ground off obliquely in the usual way. It is still better to let the lower part of d end in a series of capillary platinum tubes, all cut off obliquely, with their open mouths nearly in the same horizontal plane. Air thus enters A in a spray of fine bubbles, and the intermittence seen at B, even in the most unfavorable cases of extremely slow efSux of gas out of JB, is reduced to 0.0i<'"» and less. The air in B enters the capillary tube through the stop-cock JK", as has been said. The capillary platinum tube itself is shown at I, and is wound in form of a truncated cone, so as to be uniformly heated by the adjustable burner n immediately below it, the gases of which are carried off by the adjustable chimney L. In other words, the helix of the platinum capillary tube is so wound as to lie quite within the zone of fusion of the Bunsen burner. The outer end of the tube /commu- nicates directly with the air. The other end is soldered into a lateral arm of the tube K by means of resinous cement. In order to keep the joint cold and the inner end of the capillary at a known temperature a rapid chrrent of cold water from the hydrant flows through the cylin- drical sheet-iron box m, which surrounds the joint. Apparatus for constant pressure. — This form of apparatus was used in the earlier experiments, and the results obtained by means of it, some of which will be cited below, proved the feasibility of this method, at (898) BAftUBj VISCOSITY OP GASES. 245 least for empirical temperature measurement, beyond a doubt. In later experiments the proximity of the burner n to tbe receiver B was found objectionable, and the cramped arrangement of this part of the appa- ratus interfered in other ways with accurate measurement. Retaining the essential features of Fig. 43 the apparatus was modified as follows: In Fig. 44, jB ^ is the receiver into which the mercury flows on pass- ing out of the Mariotte flask. The lettering of this figure is in con- formity with that of Fig. 43, but the disposition chosen is such as to show additional parts. The manometer B R' B' is here very clearly given, quite filled with mercury, as is the case at the outset of the ex- periment. It will be seen that as the pressure in B increases, the mer- cury in the reservoir B' B' passes into the tube jR, leaving a vacant space in B' B' above the lower meniscus. But as the experiment pro- ceeds, and the receiver B fills with mercury, this metal eventually falls into the communication tube r, while the air displaced escapes into B through the capillary tube s. Hence each time B is filled with mercury a fixed volume of air must pass out of it, and the manometer B B' B' in- troduces no discrepancy. The cock D being closed, mercury falls into B from ^, as the column passes through the lateral tube P UQ, The top of R'R is cut off obliquely, so as to guide the descending drops or little stream of mercury at once into B. The drying-tube of the apparatus communicates with tr, and may be shut off by the faucet 8. In this way dry air or any other gas may be easily introduced. The capillary tube is here placed at some distance from B and in connection ^ith the lateral tube k. A small sensitive thermometer se<'iled in the vertical tube T indicates the temperature of the gas as it escapes into the cax)illaries. For the sake of clearness in diagram the tubes Q, 22, T are represented as placed in a single vertical plane. In practice the rubber cork is perforated symmetrically and larger tubes may be chosen. The tube P Q comes apart at CT, and hence the tubes and the manometer may be easily withdrawn from P. When in use it is necessary to seal in the cork and the divers glass tubes with resinous cement. It is easily seen that after B is full of mercury the Mariotte flask A may be lowered, and on opening the stop-cocks I) and S mercury will flow back from B to A. The receiver B is thus filled with dry gas and again ready for experiment. But the order of manipulation is import- ant, and will be indicated in connection with the data given below. In using this method of compression preferably to a method of ex- haustion, by both of which a flow of gas through the tubes can be secured, I was guided by the belief that the methods of measurement in the former case are more easily capable of variation. This the present chapter may show. Again, the tendency of the dissociated liydrocar- bon gases of the burner to i)ermeate the walls of the platinum capillary tabes at high temperatures, is of less disturbing effect when the current of gas is condensed tlian when it is rarified. T!he capillary apparatus, — In Fig. 44 there is ample room for air to (899) 246 BIEA8DREMENT OF HIGH TBMt*E»ATDEEB. tDOu-St V18C08ITY OF GA8B8. 247 pass aromid the thermometer in the tube T, and thence by the lateral tube Jc into tbe capillary apparatus. This is shown in side elevation in Pig, 45 and in plan in Fig. 46. The fignres are sectional, and the lettering of Fig. 43 is retained. Tbe scaffolding and non-essential parts are omitted. Regarding tbia figure in its gen- eral pnrposes, I will say here that there are three ways in which viscosity has been measured: 1. By measuring tbe time of efflox of tbe fixed volnmes of air in S through the capillaries. 2. By measuring tbe rate at which air passes out of tbe capillaries. 3. By differential methods. Tbe first of these methods ia not gen- erally as convenient as tbe second, t>e- canse the volume of B is relatively large, and tbe time of efBnx may become enor- mously large. Hence in my final experi- ments I nsed the second method, !ind it is to this that the present description largely applies. The gas enters from the tube k (Fig. 45) through tbe stop cock K, thence itpasses through the tube ^^ into the coil of plattuum capillary tube J, and ont of this into the graduated tube llll, filled with water. Here it is measured. The tube II II is simply an inverted bu- rette of about 60"' capacity. After fill- ing it with gas and taking the observa. tion it is made ready at once for the next experiment by sucking the water out of the pneumatic trough MM up into the tube through the stopcock o aud closing it. To insure constancy of temperature this tube n n is jacketed by a larger tnbe, iiii, through which a rapid current of water, entering by the tube p t, con- tinually circulates. The water escaping &om the bottom of iiii keeps the trough MM full of cold water, and fiually escapes by the lateral efflux pipe X. The upper vertical tube q ia used in filling iiii with (901) 248 MEASUREMENT OF UIGII TEMPERATURES. [bull. SI water at the outset of tlie experiment, and is then closed by a pinch- cock. It is easy to make the current swift enougli to keep both the tube and the trough at a constant temperature even when the helix I is heated to extreme white heat. The helix of the platinum capillary tube is wound in the form of a nearly compact spiral and with the internal radius just large enough to admit the insulator of the thermo-couple. Smaller and more compact coils are favorable to constant temperature throughout the length of the capillary tubes. It is convenient to use two or more such capillary tube, wound side by side, so as to make what may be called a fasciculated helix. The anterior ends of these capillaries are soldered to a small longitudinally perforated brass cylinder hy which is then hermetically sealed into the adit tube g h. The posterior ends of the capillaries, which, like the other ends, return to the trough .If jV, are bent slightly upward, so as to discharge the gas into 11 11, As leaks are fatal to the tempera- Fin. 46. Plan of tbe capillary appuratuH. Scale ^. ture measurement at 7, the platinum tubes must be carefully soldered into the vertical wall of the trough M 3/, through which they pass. Soldering the tubes in i)lace and sealing them is a difficult operation, and too much care can not betaken in guarding against clogging of the minute capillary canals. Moreover, solder must be kept away from the part« of I which are heated. Insufficiently cautious manipulation in this respect ruined more than one of my tubes. Unfortunately, the only satisfactory check on the degree of ])erfection of the adjustments made (902) BAfius-l VISCOSITY OP GASES. 249 is given by an inspection of the results obtained. Any flaw in the con- nections can therefore be reraedieJ only at the expense of much time. Differential apparatus. — Before passing to the method used for heating it may be well to insert a few remarks relative to the differential appa- ratus. This is closely analogous in character to a differential galvanom- eter, and the rates of transpirations through tubes, one of which is hot the other cold, are com()ared. The arrangement of this apparatus is readily seen in Fig. 46. A lateral arm, XI\ of the tube g h communicates with the cold helix P, which is completely submerged in the water of the trough M Mj and provided with its own graduated tube I' I and water- jacket i i'. Except in temperature, the capillaries and their pneumatic appurtenances are identical in form. Certain special desiderata will be indicated below. Method of heativg, — All the soldered parts of the capillary apparatus being thus thermally i)rotected by a current of water from the hydrant, the heating of the spiral is not a difficult problem. To make observa- tions at the low temperature (as near 0^ C. as convenient) a current of water may be showered upon the helix out of the water pipes. But it is equally good to siphon the water out of the trough M M, For 100^ the helix is appropriately surrounded by a nonconducting tube, through which steam circulates freely. Admirably constant mean temperatures are obtained as high as l,000o by simply heating the helix in a chimneyed Bunsen burner. For l,300o the Bunsen burner is replaced by a blast- lamp fed by a regular current of air. In the case of these high tem- peratures the helix is surrounded by a cylindrical tube of asbestus, as shown ac n n, Figs. 45 and 46. These cylinders are exceedingly con- venient and may be made by soaking asbestus board in water and roll- ing it around a cylindrical stick of •suitable diameter. After drying, the cylinders are ready for use. Parts liable to breakage are, of course, protected from radiation by asbestus screens. Such subsidiary screen- ing is everywhere necessary, and need not be described here. Great difficulties were encountered in endeavoring to obtain satisfactorily con- stant temperatures between 300^ and l,000o. After much vain search- ing I finally tried an ordinary oil student lamp for the purpose, and ob- tained excellent results. The space in the chimney of such a lamp above the flame is available for a hot-air bath. In Fig. 45, n' n' shows the position of the chimney of this lamp. The temperatures thus obtain- able, besides being constant or of very slow regular variations (increase) (903) 260 M£ASUR£MENt O^ filGfi tEMP^RATtJlE^S. [BULL. ti. may be made to dififer over quite a wide range, as is shown by the fol- lowing table : Tablb 80. — Thermal constants of the oil student lamp. cm. 2 2 2 2 3 14 14 14 9 9 3 3 14 14 Time. m. 7 14 21 10 20 30 25 30 40 60 63 4168 4201 4255 4288 7487 7593 7647 7784 10600 10690 9563 9563 11490 11490 0" o 414 416 421 423 669 681 685 695 904 904 825 825 966 956 Incipient ftuion of the glAsa chimney sarronndlng the flame. Devitrificfttion. Remarks. Very low flame. Low flame. 'HiKh flame. » Flame very high. In Table 80, d denotes the depth of the janction of the thermo-conple beU)w the top of the chimney, which top is aboat 20*^™ above the mean height of the flame. 0*\ e, denote the temperatare and the correspond- ing thermo-electric force of the thermo-couple used for measurement at the time given in the second column. The thermo-couple in this instance was No. 39 (calibrated above), and the junction, after be- ing surrounded by a little cushion of carded asbestus, was enveloped by a jacket of thin platinum foil fastened to the stem insulator. The junction is, of course, placed in the axis of the chimney, since tempera- ture decreases towards the walls. The highest temperatures are ob- tained by enveloping the chimney in the cylindrical tube of asbestus referred to above, in which case the glass is easily fused. Lower tem- peratures than those of the table may be obtained by lengthening the chimney with the asbestus tube and observing near the top. The aux- iliary tubes are suitably wired in position. In addition to the large interval of temperature, the Argand lamp has the advantage of furnishing an air bath. Since platinum is pervious to hydrogen (see below), direct exposure to the Bunsen flame introduces an error because of the hydrogen which passes through the metal. But tbis error does not seem to be serious unless the temperatures are very high. In all these cases the mean temperatures are satisfactorily constant, but it does not follow that temperature will be constant throughout the (904) ftAauB.] VISCOSITY OP GASES. 251 T#lnine of the platinnm capillary. Indeed, variations of lOQo within the spires of the helix at temperatares as high as 1,200^ are not impossible. If, however, the interior of the helix be filled with some nonconducting sabstance like asbestos fiber, and the exterior surface be snngly sur- rounded by a little box of non-conducting substance, like mica, the de- gree of constant temperature is much improved. Better results are ob- tainable by surrounding the helix with alternate layers of good and bad conductor. But in its practical application this method is troublesome, and I have therefore preferred to measure temperatures at both the ex- terior and the interior surfaces of the helix. In the final experiments two thermo-electric junctions were in contact with the outside and one with the inside of the helix. Pressures were read off in mercury columns by aid of the Grunow cathetometer already referred to. It is frequently necessary in this ap- paratus to open the stop-cocks at particular pressures. To obtain these, preliminary experiments are made {^''Ilinschiesaen^)^ and the desired positions of the meniscus are indicated by adjustable fiducial marks. ^ For the measurement of intervals of time an excellent chronometer of Brocking in Hamburg was available. , METHODS OP COMPUTATION. The general equation, — ^The computations of the present memoir are based on the Poisenille* Meyer transpiration formula, the 8i)ecial appli- cation of which to gaseous flow is due to Meyer. ^ It is available in two forms. The first form is where u denotes the velocity of a particle at a radius, r, from the axis of the capillary tube, the diameter (bore) and length of which are 2B and Lj respectively ; where Pand p are the pressures at the two ends of the capillary tube, and where ^ denotes the coefficient of internal friction (viscosity), C the coefficient of slip (Gleituug's coefficient). The second form is obtained by integration from equation (I). It contains a new variable, viz, Vi the volume of gas transpiring through any section of the tube where the pressure is pi during the time t Fi= ?0+4) <=> If this equation is to be used for the absolute evaluation of;/ it must be borne in mind that the dimensions of — —'^— are those of a pressure. Hence if P and p have been expressed in terms of the heights of col- umns of mercury, the factor 6g must be inserted in the right-hand mem- » Meyer: Pogg. Ann., vol. 127, 18G6, p. 201). 252 MEASUREMENT OF HIGH TEMPERATURES. [bull. 54. ber. Here S is the density of the mercury colaron and g the accelerji- tion of gravity at the place of observation. With this introduction the dimensions of 77, computed from equation (2), are [iwZ-^T-*], which are identical, of course, with the dimensions required by the funda- mental formula of viscosity, or by the well-known equation of Maxwellj 77=0.318p/21i, deduced in the kinetic theory of .upases. Equation (2) shows, moreover, that the dimensions of Z are linear, agreeing with the thermo dynamic interpretation of C, which is i)roportional to the mean free path of the molecule of a ga«. C has been called " Gleitung's co- efficient" bj" Helmholtz, a name, the appropriateness of which appears, inasmuch as C='^ where € is the coefficient of external fricti(m of 'the gas. Neither formula (I) nor formula (2) contain direct reference to the temperature at which transpiration takes place. Such reference is, however, implied in the 2? occurring in the denominators of ^1) and (2); for the value ofp is given by Boyle-Charles's law as p=kp(l+a6) (3) where p and 6 are the density and temperature corresponding to the pressure 21, and where Jc is constant. Eegarding the general a])plications of (1) and (2) I will say that the derivation of these equations presupposes that p and p are independent of r, or that for the points of any given right section of the tube j; and p are constant. Again it presupposes a nearly steady flow, such that the diflorential coefficients of 1*^ and /', i. e., ax du (Pu d^u rfa?' da^^ dxdr^ where x is measured along the axis of the tube are practically zero. Finally equations (1) and (2) are true only for circular sections. In the case of elliptic sections,^ with semi-axes a and h^ the equation (2) be- comes (supi>osing C=0) • .. -,r — P J- -<» O ,0% Pi ^tjL a^+b^ ' so that the equation, when a and h are not known, can only be used for the interpretation of relative measurements. Case of two cold e^ids, absolute apparatus. — Equation (2) is available for experimental measurement in a variety of ways. It presnpi>oses, however, that the temperature of the capillary tube be the same through- out its length. This is, of course, a feasible precaution, for it is only necessary to weld the platinum capillary to platinum terminal tabes J Meyer: Ibid., p. :UM ; Matthieii: C. R., vol. 57. 1863. p. 320. (UOC) «AEU6.] VISCOSITY OP GASES. 253 • of larger bore. Methods of doing this- will be described below. Such apparatus would^ however, be expensive, and in an introductory in- vestigation, in which easy variation of the capillary bore is one of the desiderata, the use of fixed forms of apparatus is unadvisable. Hence I have made use of platinum capillary tubes with cold ends in the way described in the preceding paragraph, inasmuch a« these can be drawn down from the original to any smaller radius, and then inserted into the pneumatic apparatus with comparative facilit3\ The cold ends, how- ever, introduce an error of a serious kind, for which allowance must be carefully made. Fortunately this can be done with ease and accuracy by successive applications of Meyer's equation. As before, let JK, i, ^, t be the symbols of radius, length, temperature, and time. Let the platinum capillary tube be supposed to be made up of three parts, l\ Z", Z'", so that V+l"-^l'"=L. Let the variables refer- ring to these parts be similarly accentuated. Then the following scheme of variables presents itself: Pr%K',l', 6' ;t'y7f\ etc. p' r'\R'\l'\e'\t'\?f",etc, p" V"\R"',V",^"',t"\rf"\eic, p Of the three partial tubes thus given the first and third are ends, and hence V and V" are small as compared with l"^ and O* and 6"' small as compared with the high tem])erature 0". Applied to the apparatus described, the following simplifications are admissible: R'=R'"=:R; 7/=//"=^/; 6' =6'"=. 6'^ moreover V'p'=V"fy"=^V'''p''*=zVp, and t'z=it"z=lf"=t. The successive application of Meyer's equations thus leads to . (4) Now, if ft be the mean coeflBcient of expansion of platinum, so that i2''=i?o" (1+/^ 6") {R and Ro being supposed identical), I find finally tbat rr i+4> ^R J ( n P^-f t R{^ V /-R, iG p V p - r --= If this equation is to express ?/' absolutely, and if P and p are meas- ured in heights of columns of mercury, the factor 6g must be inserted in thQ right-.band member, as before (page 252). Regarding the other quantities it is clear that they are measured in terms of c. g. s. units. The temperature of Fis 6. Equation (5) is capable of much simplification. In the above appa- ratus i?o"=i?o; hence care must bo taken either in making T)^ as small as possible, or /' and V'^ must be correctly measured. In the above apparatus very close contiguity of hot and cold i)art6 of the spiral (907) 254 MEASUREMENT OF HIGH TEMPERATURES. [buli-M. • is secured by the use of ranning water in the way described. Moreover 1/ is small as compared with rf'^ becaase long ranges of temperature are (1? //\ 4 -^- j it is obvious that the corrective factor may be made to vanish specklily by selecting terminals of larger bore. If 6=z6^\ and therefore ri=Vf'^ equation (6) reduces at once to equation (2), supposing of course that Ro"=:Eo' Case of two coldeful^j differential apparatus. — With this result in hand the question with regard to the equations applying to differential a- rat us of the kind sketched above (page 250) is next in order. For the case of the hot helix there applies as before T "~l 16 « V V' "^ and for the cold helix, the temperature of which is uniformly 0, whence, very nearly, 1+4C 7 Now, if the two helices be identical in radius and length, and iftlie times of transpiration be also identical, then, since t=t,; L,=L; Ro"= R^=R,', rt' fj'-=i+aO" l'+l"' ^^+^^^ <^' 1+iZ/R. ^ ~ Ij Again, if as before, R"o=Ri,=Rc, and L=L,, but the same volumes are found to transpire in the times t and t^ ; then, since F= V, 4C'' t I'+l"' ~~liC ^ — IT" (908) BARU8.) VISCOSITY OF GASES. 255 Finally, if 0=6" equation (6) furniRhes a very simple eqaatiou for the nitio of radii of capillary tubes. For if t:=t^ ©■= VL a relation which is frequently of use. K8TEBIMENTAX RESULTS. Manipulation. — In describing the present series of experiments it will be advisable to proceed somewhat explicitly ; for the methods were fre- quently varied, and variations of an apparently trifling kind were fre- quently found of great practical importance. Neither is it expedient to retain wholly the chronologic order of experiment. The following tables, 81 to 89, represent a connected series of experiments, in which the method used is gradually perfected, and in which the data therefore approach the true law of variation more fully as the experiments proceed. In making these experiments the apparatus, Figs. 44 to 46, was used. The air which had transpired was therefore caught after efflux from the capillary tubes. Inasmuch as the receiver B is very large (550^^) and transpiration through the capillary tube takes place at a very slow rate, almost no effect is produced in the pressure of the gas in B when the cock K (Figs. 43, 46) is opened. This is a great convenience in manipu- lation and suggests the following scheme of operations : Suppose the Mariotte flask to be in its lowest position on the standard, aaaa bbbbj all cocks except ^ open, and the Mariotte uncorked. Mercury will then have run back into A^ and the reservoir B will be filled with dry air. Now, close the cocks C and 8 and cork tlie Mariotte. Hoist the flask A to the level above B desirea, and clamp it. Open G slightly at first until the mercury is seen just above D and then close 2>. Mercury will then flow into B through P U Q (the cock C being now fully open) until the maximum pressure is registered by the manometer R R'B'. Both the lower and upper meniscus of this are read. The gas in B is therefore practically under the pressure under which it is to be passed through the capillaries. Inasmuch as the volume of B is more than ten times as large as the volume to be measured after efflux, the pressure appa- ratus is ready for a number of consecutive experiments. After the receiver is quite filled with mercury and the cock JT is closed, C is closed also and the Mariotte flask is lowered and unstopped. /> is now opened and is opened cautiously, so as to take the pressure out of the ma- nometer. After this is done 8 is opened, whereupon G may be fully opened and the mercury thus flows back to A, while B fills with dry air. The operations are then repeated and the gas in B is put under pressure for the next ten experiments. This is the mode of experimen- tation in the main, although accidents or divers special purposes suggest slight variations of it. It is desirable to draw no air through the ma- (909) 256 MEASUREMENT OF HJGH TEMPERATURES. Tbull. 54. nometer R R' R'] for not only will sucli air be moist, but the mercury hurled out of R' R* by bubbling displaces Xh^ lower meniscus to a seri- ously low level some times. During the experiments the lower meniscus remains constant in level. Hence the upper meniscus need be read only for the detection of slight variations, and the fact that the lower menis- cus is finally hid by the surrounding mercuo' is no disadvantage. Nomenclature. — The results were computed from equation (6), on page 254. The data in the table are similarly designated, and their full sig- nification is as follows: P is the pressure of the gas at influx, i. e., when it enters the plati- num capillary. P therefore is the zero height of the mercury column in the manometer plus the zero height of the barometer. Coixection is to be made for ca))illary depression of the upper meniscus of the ma- nometer. Correction is also to be made for optic displacement of the lower meniscus of the manometer when seen through the walls of the reservoir B (Fig. 44). As the mean effects produced by these two errors were in an opposite sense, and nearly- the same in magnitude, I did not apply them. Moreover they have no effect on F (6*% p is the pressure of the gas at efilux. Hence it is equal to the zero height of the barometer increased by the mercury value of the depth of the efflux tubes below the level of water in the trouerh. Perhaps p ought also to have been increased by the capillaiy reaction effect of water at the point of efflux. But as I could not estimate this, I u^ed large values of P in order to secure as steady and rapid a flow as per- missible. t is the time which corresponds to the volume of gas Vq measured after transpiration. It is usually advisable to make t nearly constant and measure the variation of Vq. The time errors made in opening and closing the stopcock K are not larger than one-fifth of a second. Hence t can be measured sharply. Vq is the volume of dry air escaping at the normal pressure 76<^" and temperature 0° G. V (page 248) being the true variable, some pains must be taken in correcting it. In the first place, inasmuch as 7 is meas- ured over water, it must be reduced to dryness, to zero centigrade, and to 76*^*". This is conveniently done by the aid of Landolt and Boern- stein's tables, it being remembered that I^is under atmospheric pressure minus the mercury value of the residuary column of water in the bu- rette lllL Finally V must be corrected for the solubility of the gas, which in case of air may be neglected, bnt in case of hydrogen is as large as 2 per cent. Formula (5), however, calls for V at 6 and jp. Hence, if Vis reduced at once to 0° and 70*^^"' by tables, it is convenient to transform formula (5) into . , , r"""Lio " 70 Wi'' 1+4; V A'o / l""} i+av ^ K" R (910) «ARU8.) VISCOSITY OF GASES. 257 Yp which easily results since .^ , .^ =76. F©, and the effect of {1+aO) on the corrective member of formula 5 may be neglected, when d is small. Finally, Fmust be corrected for the amount of air left in the adit tube g hy after the cock is closed. To reduce this dead space to the smallest value it is desirable to fill up the tube g h partially with glass rod. The residual space is easily measured, as follows : Let v be this residual volume. Then, if in the time f, which elapses between opening and closing the cock k, the volume V escapes into the measuring tube, the volume ultimately found there is a= V+v. Again, if during the same time t the cock had been opened and closed n times (delays of opening and closing supposed to be allowed for) the volume found in the measuring tube is 6= V+nv. Hence • 6— a=s:(w— l)v whence v may be found. is the temperature of the cold ends V and V" of the capillary as well as the temperature at which the wet air in the burette is measured. It is determined by submerging a thermometer in the trough MM. 6" is the temperature of the hot part I" of the platinum tube. Be- mark8 concerning its measurement will be found with each table since this variable is the difficult one to evaluate correctly. The measure- ment of the actual value of 6^" is directly dependent on the degree of constant temperature in the helix. Kj finally, denotes the radius of the capillary tubes. It is this quantity which, in case of fine opaque capillary tubes, it is exceedingly difficult to determine. In some of the experiments below I subsequently filled the tubes with mercury in ways there to be indicated, and weighed the thread. But in the experiment, Tables 81 to 89, 1 did not wish to en- danger the platinum tubes by employing this method. Nor did I think it safe to apply volumetric methods like those described on pp. 195, 214. The only procedure left therefore consists in weighin r (mass m) known lengths, I/, of the capillary, and measuring the external diam- eter B„ by screw calipers. From the known density 6 of platinum the internal radius B may be calculated at once in its square value as Unfortunately this is a crude method at best, and the problem is even wore seriously difficult, because formula 6 calls for the fourth power of B. Flence the absolute values of ;/' and t; in the table are distorted ; but since this distortion is uniform for all data, and since it does not therefore affect the relative values, the errors introduced by incorrect B do not interfere with the chief purposes of the present investigation. The attempt to obtain absolute values from metallic' capillary tube^ BuU, 64 17 (911) 258 MEASUREMENT OF HIGH TEMPERATURES. Ibull.54. is perhaps futile. It is impossible to guaranty that in such tubes the radius is either rigorously uniform throughout the length of the tube or that the capillary canal is truly circular in section. Coiling of tubes, so essential in very high temperature work, also flattens the section. In drawing tubes flaws or splinters of metal partially projecting into the capillary canal can not always be obviated. But all these effects are not hurtful where relative results are alone of interest. This is, of course, the case in pyrometry. Hydrogen and air, as used in the following tables, are not intended to refer to absolutely pure gases. Both gases were dried, of course, in the usual way. But the hydrogen may contain traces of air or sul- phide, and the air was not freed from carbonic acid. My object in the following experiments was to test the possibility of an identity of law in the case of two thoroughly different gasesy the zero properties of each of which were continually redetermined, i. e., before eaeh exx)eriment. luiismuch as these gases are to be true gases, all vaporous constituents were to be excluded. At high temperatures, however, even this pre- caution is not essential. Data. — Tables 81 and 82 contain the results of consecutive series of experiments made with air and with hydrogen, respectively. In these early experiments I did not venture to solder the terminals of the helix into the walls of the pneumatic trough from fear of injury to the tubes. Hence the trough leaked at high temperatures, and the water wetting the outside of the asbestus chimney or furnace which surrounds the helix and burner was the cause of an Irregular distribution of tem- perature, which I did not foresee. Temperature being measured in the inside of the helix at a point nearest the trough is therefore decidedly low, for it is here that the effect of cooling the en- vironment is seriously felt. The position of the thermo- couple (No. 37, calibrated above) is nearly that given in Fig. 47. Moreover, the helix itself is naked, that is, not jacketed by an envelope of mica or other substance of low thermal conductivity. Temperatures near 1,00(P are ob- tained by direct exposure to the flame of the chimneyed Bunsen burner; higher temperatures (usually above l,200Oj by exposure to the flame of the air-blast lamp. Tempeni- Fio. 47. Vertical turcs below 800^ (usually) are obtained in the air bath nectionthrongh Qf i\^^ petroleum Argand burner, the chimney of which bclix. Scale i. . .. t , . * , ^ , IS suitably jacketed. (912) BABU8.] VlSCOSIXy. OP OASES. 259 Table 81. — Fieoosity of air, Platitium capillary, Thermo-^iauple 2fo. 37. [Capillary tabe No. 10. i=33.43'«. J' + l"=4.4«. iw = 0.0002508. tf = 6o. iZ=0.00794'«.] L 124.28 124.28 124.28 88.49 88.40 88.49 88.69 124.66 124.68 124. 76 124.83 124. .'il 1^4.64 124.64 124. &t 124.63 124.61 124.61 124.77 124.84 124.87 124.51 124.55 124.55 124.73 124 28 124.00 124.01 124.01 124.03 124.03 124.77 124.77 124.77 124.77 124.53 124.53 124. 53 124.53 Oo. .•«) 88.31 8a 31 88.29 p t" Fo $" 76l02 165 49.11 6 76.02 162 48.95 6 76.02 160 48.26 6 75.92 770 47.91 6 75.92 810 60.27 6 75.92 796 50.30 6 75.92 810 61.34 6 75.92 155 47.28 6 76.92 160 48.20 6 75.92 160 48.50 6 75.92 160 48.50 6 75.95 725 48.43 430 75.95 725 47.73 442 75.95 760 49.11 456 75.96 760 48.11 464 75.95 780 48.39 472 75.96 785 47.59 483 75.95 810 48.44 490 75.96 935 49.85 558 75.96 905 48.63 564 75.95 900 4&49 652 75.95 905 48 68 546 75.95 900 48.44 545 75.05 1485 49.74 840 75.05 1470 49.64 828 78.19 1655 50.16 880 76.19 1660 47.66 871 76.19 1620 49.91 861 76.19 1690 48.56 866 76.19 2080 47.67 1141 76.19 2110 48.08 1136 76.39 20f0 48.56 1127 76.39 2070 49.16 1126 76.39 2085 50.04 1114 76.39 2040 49.30 1104 76.29 160 48.75 6 76.29 160 48.71 6 76.29 160 48.65 6 76.29 160 4&71 6 76.29 840 60.49 6 76.29 840 50.60 6 76.29 840 50.60 6 76.29 840 50.4 9 6 r 1+4 ^"/-B" 0.0002592 2663 2558 0.0002618 2625 2570 2615 0.0002557 2585 2580 2684 0.0006255 6266 6276 5324 6370 5425 5463 0.0005670 5674 5664 5669 5665 0.0006824 6869 0. 0007221 7163 7162 7201 0.0007829 7903 0.0007771 7765 T732 7802 0.0002546 2548 2651 2648 0. 0002619 2627 2627 2628 1X9") 2.096 2.100 2.106 2.123 2.142 2.164 2.179 2.262 2.263 2.259 2.261 2.259 2.722 2.740 2.879 2.856 2.865 2.871 3.122 3.151 8.099 3.006 8.083 3.111 (913) 260 MEASUREMENT OF UIGH TfeMPERATUBES. [BULL. 54. Table 82. — Viscosity of hydrogen. [Ci^lllary tube No. 10. i=:33.43"". I'+I'"=4.4"». i^,=0.0001392. fl=7o. i2=O.00794~.] i 124.96 124.96 134.96 88.72 88.71 88.73 88.76 124.61 124.62 124.62 121.61 88.56 88.60 88.62 124.53 124.54 124.58 125.49 125.53 125.53 125.62 125.55 126.63 125.69 126.71 126.55 ,126. 67 126.67 126. 68 126. 70 126. 70 126.09 126.70 126.68 126.53 126. 57 126.64 77.29 77.29 77.29 77.29 77.29 77.29 77.29 77.29 77.29 77.29 77.29 77.29 77.29 77.29 77.29 77.29 77.29 77.26 77.26 77.26 p t" F. »" 76.72 90 49.43 6 76.72 90 49.47 6 76.72 90 49.49 6 76.72 480 50.93 6 76.72 485 51.58 6 76.72 480 51.30 6 76.72 450 48.06 6 76.72 90 49.34 6 76.72 90 49.56 6 76.72 90 49.60 6 76.72 90 40.51 6 76.72 480 50.78 6 76.72 460 40.15 6 76.72 480 51.39 6 76.71 365 40.73 392 76.71 360 48.62 380 76.71 360 43.37 428 •" l+4<'7^" 0. 0001419 1418 1418 0.0001497 1478 1488 1491 0. 0001409 1403 1402 1404 0. 0001481 1472 1470 0. 0002749 2747 2874 Frefth hydrogen supplied. 380 385 395 420 420 420 440 530 565 570 600 600 780 780 780 780 815 1050 1035 1020 49.09 49.49 49.65 50.51 49.49 48.59 49.62 50.26 48.80 48.22 49.69 48.12 4&40 49.19 48.89 48.89 50.92 48.91 48.98 48.86 I 398 411 424 437 452 461 474 565 634 644 658 668 848 834 835 834 834 1006 097 994 0. 0002792 2810 2822 ' 2899 2905 2032 2968 0. 0003251 3300 3293 3470 3446 0. 0003807 3766 3786 3791 3790 0.0004438 4404 4366 F(B") 1.975 1.974 2.065 2.006 2.019 2.028 2.0&1 2.087 2.107 2.133 2.330 2.371 • 2.366 2.493 2.476 2.735 2.706 2.720 2.723 2,730 3.189 3.165 3.136 Immediately after the high-temperature measurement. 120.32 126.32 125.35 125.40 77.26 90 50.60 7 0.0001415 77.26 89 50.19 7 1414 After a day. Freah hydrogen supplied. 77.43 90 48.98 7 0.0001424 77.43 90 49.02 7 1425 Fresh hydrogen supplied. 126.02 77.43 90 4H. no 7 125. 02 77.43 90 4H.45 7 125. 03 77.43 00 48.49 7 125.06 77.43 90 4.-. 52 1 0. 0001425 1428 1427 1427 ^9U) BARUB.] VISCOSITY OF GASES. 261 Table 82 — FUcosHy of hydrogen — Continued. p P 77.43 77.43 77.43 77.43 t' n 0" F(B") 125.07 89.43 89.41 89.42 90 480 480 480 48.52 4&56 4a 62 48.98 7 7 7 7 1428 0. 0001579 1574 1564 m Bearing in mind therefore that the carve Z" F(d")= 'R> 1+4 as given by these results, is necessjgrily bigh, I constructed F{6") both for Table 81 and for Table 82. The result shows a most surprising degree of coincidence in the values for air and for hydrogen, proving beyond a doubt that the same law of variation F((^') must apply to both gases. Since the locus constructed falls below (l+a^')*, where £r=0.003665, the coefficient of expansion of gases, the true value of F{6'') must fall decidedly below (l+ac^'')i and a fortiori below the formula ^/'« Vo =1+0.002751^-0.00000034^2 by which Holman reproduced the data of his fine observations for air betweeh 0^ O. and 100^. Now, although the data in the locus drawn fall below (l+a^')2, it can not at once be assumed that (l+ad")i is to be discarded as the value of ' ; for in view of the occurrence of the factor Vo ^1 r// ' 1+4,. where C is essentially positive and increasing with ^", it does not follow that F(ff') and '^' are identical. The curve shows the effect of a cold environment in a very striking way; for the Bunsen-burner temperatures here lie at only 850^, and 1,140^ is the highest temperature reached by the blast-lamp. Clearly the mean temperature of the thermo-couple is only a nominal value for the mean temperature of the helix of platinum tube. This is proved by the high values of F(f^^^) for hydrogen at 1,000^ ; for these large data are due to the fact that platimuu is pervious to hydrogen, an effect which, in the following tables, does not produce a serious discrepancy until much higher temperatures are reached. (915^ 262 MEASUREMENT OF HIGH TEMPERATURES. [BULL 54. In Tables 83 and 84 results are given for hydrogen and air, resjiect- ively , with an improved form of apparatus. The thermo electric junction still occupies a position near the center of figure of the helix and pro- tected from direct action of the flame by a flat plug or pellicle of asbestns (Fig. 47c); but- the terminal tubes of the helix are soldered into the walls of the pneumatic trough, through which they project. In this way a leakage of water is prevented, and the chimney of the burner remains dry and of uuifrom temperature. The helix, however, is naked here, as in the foregoing experiment. Table 83. — Viaconty of hydrogen. [Capillary tube No. 10. I/=33.43«. V + 1'" = 4.4'-. » = 0.0001416. « » 6. R = 0.00794». 1 p P t" Fo 0" 1-H<"/R" F{$") 123.97 123.97 123.97 123.97 123.98 123. 82 123.83 123.81 123.83 123. K> 123.83 123.88 75.66 75.66 75.66 75.66 76.66 75.66 75.66 75.06 75.66 76.66 75.66 75.00 95 90 90 90 90 90 90 90 90 90 90 440 51.^ 48.73 48.70 4&80 48.78. 48.33 48.37 48.42 48.37 48.39 4&37 50.04 6 6 6 6 6 6 6 6 6 6 6 482 0. 0001427 1426 1427 1424 1425 0. 0001432 1431 1429 1431 1431 1431 0. 0002813 1.986 123.00 75.60 440 40.83 490 2831 1.999 123. 92 75.60 440 40.64 490 2»42 2.007 123.92 75. CO 440 49.61 504 2867 2.021 123.92 75.60 440 47.89 511 2874 2.030 123.67 7.'i. 62 630 50.63 671 0.0003244 2.291 123.68 75.62 660 50.96 695 3307 2.336 123.64 75.62 660 50.23 705 3320 2.345 123.64 75. 62 75.62 75.62 680 660 50.93 715 0.0003340 3295 2.359 2.327 12:1. 85 51.75 688 123.85 75.62 660 51.55 691 3-209 2.330 123.85 75.62 660 50.93 700 3306 2.335 123.85 660 50.14 • 707 3336 2.356 121. 75 75.72 1115 50.82 085 0.0004162 2.939 121.73 75.72 1115 50.77 985 4165 2. Ml 124.64 76.25 1080 50.82 1010 0. 0004231 2.987 124.63 76.25 1080 60.73 1010 4237 2.992 124. 81 76.25 1080 61.10 1007 4237 2.992 124.83 76.25 1080 51.19 1005 4238 2.993 124.84 76,25 1080 51.21 1006 4234 2.900 124.65 76.32 15G0 51. 24' 1222 0. 0005254 3.710 124.64 76. 32 1560 61.26 1227 5189 3.664 124.65 76.32 1560 61.45 1224 5228 3.692 124. 79 76.-32 1500 52.23 1223 6176 3.655 OJIG^ BARUB.] VISCOSITY OP GASES. 263 T^BLK 83. — ViscoHty of hydrogen — Continned. p P t" Fo 9" 11" F{9") 1+4<'7K" 134.31 124.31 124.31 124.31 124.31 123.99 123.99 124.03 124. 00 76.35 76.35 76.35 78.36 78.35 76.37 76.37 76.37 76.37 90 96 95 95 95 95 95 95 95 47.52 50.56 50.85 50.96 50.96 50.51 50.50 50.47 50.51 5 5 5 5 6 5 5 6 5 0.0001464 1453 1444 1441 1441 0.0001441 1442 1444 1442 Table 84. — Viscosity of air. [Capillary tube No. 10. L = 33.43». l'-\-l"' = 4.4«-. • =0.0002472. • = 5». JJ = 0.00794—.) p P t" i Fo 1 9" v F(0") 1+4^'/^" 125. 24 77.08 77.08 165 165 61.31 51.31 6 6^ 0.0002517 2517 125.24 125.23 77.08 77.08 77.08 77.08 77.08 T7.08 77.08 77.08 76.97 165 165 165 165 165 165 165 165 560 51.96 51.46 51.36 51.52 51.16 51.16 51.22 51. 22 60.77 5 5 5 6 5 5 5 335 2514 2509 2515 2514 0.0002514 2514 2511 2511 0.0004385 125.23 125.25 125.36 125.08 125.08 125.08 125.08 124.93 1.774 124. 93 76.97 780 51.90 473 4925 1.993 124. 95 76.97 740 52.20 448 4805 1.944 124.77 76.80 810 51.83 491 0.0005035 2.037 124.77 76.80 810 51.11 499 6050 2.043 124.74 76.80 880 51.57 536 5201 2.104 124.73 76.80 920 51.43 563 5285 2.138 124.73 76.80 945 51.67 575 5331 2.157 124.77 76.80 980 51.57 585 6377 2.175 134.76 76.80 980 51.94 595 5391 2.181 124.04 76.19 1680 50.62 9)0 0.0006910 2.796 124. 08 7a 17 1665 51.42 917 6836 2.766 124. 05 76.13 1665 50.98 919 6882 2.784 123.97 70.05 1665 51.15 914 6883 2.785 123.88 75.97 1665 5L61 912 6822 2.760 123.69 75.79 2780 51.21 1337 0.0008598 8.479 123.65 75.71 2820 50.87 1337 8784 3.554 123.64 75.66 2860 50.81 1337 8925 3.6U 123.60 75.62 2880 50.85 1140 8966 3.627 123.37 75.97 75.97 75.97 75.97 75.97 165 165 165 1G5 165 50.10 49.99 50.15 50.03 50.09 5 5 5 5 5 0.0002500 2505 2498 2505 2503 123.37 123.37 123.40 123.40 (Oil) HEASUBEMENt OF HIQU TEHPBRATUfifiS. i 1 1 ' i \ ' J \ \ - 1 1 i • f '- V, )''\ I . L r 1 ■ I ^ \ \ I \ \ 1 \ 1 1 V \ |J \ V , \^j ^ V \rf jj_ TheBO resalts (Tables 83 and 81) juHtify the predictions made, relative to tlie liurtfiil character oftlieleak. Fovii F(,0") he cou- structed it falls decidedly below the earlier carve. Below 1,000°, moreover, the air and liydrogea loci show a striking degree of coiiicidence (see cbart, Fig. 48), substantiating tbe earlier infer- ence tbat F (B") bas the same value for these two gases, and that the value of B", thermoelec- ttically measured, is notthetme mean temperature at which trans- 8 piration actually occurs. Above I 1,000° the air and hydrogen I curves diverge ; but this is due ■5 to the fact tbat platinum ismucb J more pervious to hydrogen than a to air. Agaii],inconseqoenceof 1 the tendency of tbe gases of the ^ burner to enter the tubes, as well I as tbe relatively large negative I errors of^'at high temperatures, ^ tbecurvatnreofbothlocichanges I from concavity downwards be- ^ ^ low 1,000° to concavity upwards abovel,000°. Hence above 1,000° i ^ tbe true character of ■^" /tin is a marred by the occurrence of dif- fusion across tbe walls of the platinum capillary tube. It ap- pears from tbe data, at extremes of high temperature {hydrogen fr=l,22r)0 nearly, air ^=1,335° nearly), tbat the large distortion pi-oduccd by diffusion is never- theless of a determinable kind. It may therefore be eliminated by applj-iug suitable corrections, as wilt be stated below. The oc- cun-euce of the consecutive high- temperature points, lying nearlj vertically one above another, is due to tbe fact that tbe non- bARlM.] VISCOSITY OP GASES. 265 registered temperature at the outside of the helix continaes to increase long after the internal and registered temperatnre is practically station- ary. The mean temperatnre of the helix is thus still on the increase, after the temperatnre of the thermo-couple is constant, and the discrepancy in question points out an ordinary phenomenon of heat conduction. All these peculiarities appear clearly in Fig. 48, where points dashed up- ward refer to hydrogen, points dashed downward refer to air. Leaving the exceptional values out of consideration, the data of these tables are of special importance. They show that the locus F{0*') does not only lie below {1+a 6"% but that its value is most probably {l-\-ad")^. Indeed, the close coincidence of the data between 400^ and 800° with the function (l+a6")l is an exceedingly striking observation. When it is called to mind that theoretical reasons suggest the exponential r form (l+a d"Y^ that the effect of slip 1+4 ^ is in the opposite sense to the necessarily negative error in ^', then the acceptation of {1+a d")l as the simplest convenient expression for the co-ordination of all the data F(6'') is easily justified. Tables 81 to 84 have proved beyond a doubt that the predominating error in the present experiment is introduced by the fact that the mean temperatures of the viscosity pyrometer and of the thermoelement are essentially different. The degree of constant temperature throughout the space occupied by these two instruments is therefore by no means suf&cient ; hence I made a few measurements on the effect produced by changing the position of the thermo couple and of enveloping the helix with layers of a nonconducting material. I also endeavored to test in how far a more reliable temperature datum could be obtained from the simultaneous indications of two or more thermocouples touching dif- ferent points on the inside and on the outside of the helix. Table b5. — Viscosity of air. Miscellaneous tests. [CapilUry tube No. 10. X=33.48«". i'+i'"=4.4«" j|o=0.0002472. •=6». i2=0.007M«-.] ill r 1+4^/22 F(9") L^Thermo-coaple nearly naked. 123.11 75.93 170 61.35 6 0.0002497 123.13 75.03 170 61.35 6 2499 123.15 75.93 170 61.40 6 2497 123.17 75.93 170 61.38 6 2500 123.17 75.93 170 61.38 6 2500 124.20 75.80 1800 61.60 1055 0.0006716 124. 31 75.80 1960 61.60 1040 7369 124.30 75.80 1845 51.00 1062 6933 124.17 75.89 2460 50.96 1347 0. 0007684 124.22 75.82 2460 50.50 1338 7813 124.27 75.79 2460 60.39 1336 7852 2.717 2.977 2.805 3.109 3.161 3.177 (9U)) 266 MEASUREMENT OF HIGH TEMPERATURES. [bull. 54. Tablb S5,—Viscoaity of air. Miscellaneous tests— Continned. p v Fo S" F{$") II. — Two thermo-coaples toaching the inner face of the naked helix. 125.30 76.95 165 61.38 6 0. 0002514 125.29 76.95 165 51.38 6 2513 125.29 76.95 165 51.35 6 2514 125.31 76.95 165 51.45 6 2511 125.40 76.95 165 51.68 6 2506 124.97 76.89 1780 52.74 964 0.0006947 124.95 76l84 1740 51.69 962 6942 124.89 76.80 1770 52.47 969 6966 124.85 76.76 1740 52.05 956 6917 124.75 76.66 2520 51.30 1224 0.0008453 124.78 76l62 2580 51.31 1227 8594 124.92 76.59 2700 5L51 1231 9028 2.811 2.809 2.819 2.789 3.420 3.477 3.053 m. — Temperature measnred inaide and (by contact) outside. 124.71 124.67 124.70 76.61 76.58 76.60 2940 1800 1800 51.50 51.38 51.07 { 1S80 1233 1132 1035 974 jo. 0009340 |o. 0006677 jo. 0007021 3.778 2.702 2.841 In the first part of Table 85 the coaple is inserted into the helix^ with it8 junction near the base, so as to be played upon directly by the flame of the bnrner. The temperatnres so obtained fluctuate in value over so large an interval that it is difficult to get a fair mean value. This appears from the wide distribution of the points obtained on the carve. Their mean position, however, is unmistakably below {l+aff")iy a result consistent with the results of the foregoing tables, inasmuch as the error of F{6^') is here positive, because the error of ^' is positive. The helix in these experiments was naked. In the second part of Table 85 two thermocouples are inserted touching the inner face of the helix, with their junction at points re- spectively nearest to and farthest from the walls of the trough. The results indicate a series of points at 900^, which are nearer the corves than before, whereas the results at 1,230^ are abnormally high. Com- paring the temperatures at the two points of the internal face, I foand 0i"=lj255^ and ^2''=l,235o, go that even at the temperatures of the blast-lamp the diflerences of temperature for points on the inner face of the helix are not of serious magnitude. The discrepancy must therefore be looked for in thermal diflerences between the inside and outside faces of the helix. In the third part of Table 85 measurements of the kind just specified are given. The two figures under f^'* arc thermal data for the inside (Ol'O) BABt7B.J VISCOSITY OF GASES. 267 and outside faces of the helix, the latter being obtained by touching the surface with the junction of a thermo couple. The discrepancies thus obtained are alarmingly large (15(P); and although this datum can be only a superior limit for the discrepancy in question, it neverthe- less points emphatically to the necessity of resorting to better means of insuring constancy of temperature throughout the space occupied by the two pyrometers. The final values of F(d") in this table are again abnormally large, so as to suggest that some vitiating error escaped detection. Comparing the thermo-couple which had been used in all these e:^periments with a fresh couple, I found mean values for the temperature of the Argand air bath, 6/1=8220 and ^2'' =804^, so that the result of repeated and prolonged firing can not have exceeded 20^. /The irregular results of Table 85 show the importance of jacketing the helix with non-conducting material, and of using at least three thermo-couples for the evaluation of 6'\ One thermo-couple on the inner face is sufficient, but at least two are necessary to measure temperature at the external face. In Tables 86 to 89 the external face of tbe helix is enveloped by a layer of mica, pressed against the surface by platinum wires, drawn tensely around the mica. In Fig. 47a the helix of platinum capillary tube is shown at 6, the surrounding envelope of mica at a. The junc- tions of the thermo-couples placed at 1, on the inner face of the helix, pressed against it by a plug of asbestus, c, and at 2 and 3 between the outer face of the helix and the mica envelope. Junctions 2 and 3 are pressed against the helix by the external platinum wiring, which holds the mica jacket in place. Fine plates of mica insulate the ends of the thermo-couples from the helix above it. The stem insulators described on page 95 are of service in keeping the wires apart. In the tables, 6i" denotes the temperature at the internal, fi^'' the mean temperature of the external face. To secure identity in the thermo-electric indica- tions the old junctions were cut off and new junctions were fused for each of the couples, Nos. 37, 38, 39, used in the measurement. The calibration of these was effected above. Chapter IV. Table 86.— Fi«oo«t/jy qf air. (Capillaiy tube No. 10. X-33.43*-. l'+«'"=4.4«-. i;j=0.0002491. •=70. i?=0.00704».J p P f Fa Bi" V n" F(&") l+Ai"/Ji" 124.00 124.00 124.00 124.00 124.01 123.51 123.45 123.38 76.08 76.08 76.08 76.08 76.08 75.02 75.87 75.81 165 165 165 165 165 1760 1760 1740 40.05 40.83 40.84 40.04 40.04 51.85 51.00 51.36 7 7 7 7 7 084 083 084 1007 1004 1004 0.0002626 26;t2 2532 2527 2528 0.0006603 6666 6654 2.687 2.676 2.671 (921) 268 MEASUREMENT OF HIGH TEMPERATURES. [BULL. 54. Tablb 86. — Viscosity of air— Continued. p P t" Fo »i «. l+4^"/ii" F(0-') 123.32 75.75 2339 51.05 1200 1224 0.0007757 3.114 123.29 75.72 2340 50.48 1204 1230 7820 8.139 123.25 75.67 2340 50.76 1204 1233 7765 3.117 123.39 75.68 860 52.69 515 525 0.0904977 1.998 123.65 75.68 890 50.91 557 567 5114 2.053 123.61 75.68 910 51.00 657 678 5068 2.082 123.58 75.68 930 50.79 580 592 5210 2.091 123.61 75.68 960 51.37 592 604 C254 2.109 123.36 123.37 123.36 123.36 123.33 74.73 74.78 74.73 74.73 74.73 165 165 165 165 165 49.59 49.59 49.50 49.59 49.63 8 8 8 8 8 8 8 8 8 8 0.0002547 2547 2552 2547 2543 Table 87. — Viscosity of hydrogen, [Capillary tube No 10. i=33.43«». l'+l"'=4.4«'. 11^=0.0001294. B=8fi. i2=0.OO7tM«».]| p P 74.71 74.71 74.71 74.71 74.71 74. f 2 74.62 74.62 74.62 74.62 74.69 <" Fo •," 8 8 8 8 8 8 8 8 8 8 970 r," Fin H4i"/li" 122.48 122.49 122.50 122.50 122.50 122.20 122.22 122.24 122.22 122.24 122.30 90 88 88 88 88 88 88 88 88 88 885 50.66 49.81 49.79 49.69 49.68 49.51 49.51 49.55 49.62 49.58 50.11 8 8 8 8 8 8 8 8 8 8 947 0.0001330 1323 1324 1326 1327 0.0001323 1324 1324 1320 1323 0.0003525 2.725 122.30 74.78 870 49.10 948 972 3528 2.726 122.32 74.75 870 40.02 948 976 3529 2.727 122.36 74.81 875 49.25 946 978 3533 2.731 122.43 74.86 900 49.68 955 984 3584 2.770 122.97 74.93 1340 49.64 1196 1228 0.0004588 3.546 122.94 74.96 1350 49.96 1202 1228 4577 3.538 122.96 74.99 1350 50.39 1192 1226 4556 3.521 124.56 76.86 495 51.65 526 538 0.0002924 2.260 124.56 76l86 405 51.09 531 544 2039 2.271 124.56 76.86 495 50.83 535 547 2939 2.271 124.54 76.86 495 50.48 536 552 2952 2.281 124.56 76.86 495 50.18 541 554 2960 2.287 124.58 76.86 495 50.09 544 556 2957 2.285 125.09 125.08 125.09 125.08 125.09 77.08 77.08 77.08 77.08 77.08 85 85 85 85 85 50.28 50.28 50.30 60.28 50.28 8 8 8 8 8 8 8 s 8 8 0.0001304 1304 1304 1304 13U1 1 (922) BAitue.] VISCOSITY OF GASES. 269 Tablb 88. — Viscosity of hydrogen. (Capillary tube No. 10. 2>=83.4a«. i'-H'"=4.4— . i|^= 0.0001294. 9=T>. I2 = 0.00794"'.J 123.80 123.82 123.31 155.27 155.27 155.27 155.30 155.30 155.27 155.25 155.45 155.35 155.45 156.10 156.07 156.05 156.07 76.05 76.95 76.95 76.55 76.55 76.55* 76.55 76.55 76.55 76.55 76.59 76.59 76.59 76.67 76.67 76.67 76.67 90 00 90 360 860 860 360 440 450 450 450 450 450 890 890 890 870 7b 50.00 50.00 50.00 50.82 50.42 50.02 49.67 50.89 51.37 51.23 50.87 50.57 50.63 ft 50.89 51.00 51.43 50.01 »l" ««" 7 7 7 7 7 . 7 410 418 412 420 416 425 420 426 604 510 509 516 512 510 514 5^ 516 525 517 526 954 956 954 953 952 951 946 946 r P(0 l+i^'/E" a 0001332 1338 1333 0. 0002518 1.946 2529 1.954 2536 1.060 2547 1.968 0.0002741 2.118 2747 2.123 2747 2.124 0.0002762 2.135 2770 2.141 2766 2.138 0.0003685 r.809 8629 2.805 3606 2.787 3601 2.783 Tadlb S9»^Viscosiiy of air, (CapUIary tub© No. 10. X=33.24«-. Z'+i"'=4.4«». i}o= 0.0002401. 0=8°. -B=0.0794«».] p P t" Fo •i" 0^' 1?" Ti9^ l+4<"/ii" 125.50 77.01 165 50.72 7 7 0. 0002579 125.61 125.53 77.01 77.01 165 165 50.75 50.72 7 7 7 7 2579 2581 124.71 76l87 710 51.10 424 436 0.0004820 1.935 124.71 76.87 710 5U.22 430 443 4865 1.9G3 124. 69 76.87 735 51.03 439 453 4995 2.005 124.65 76.87 750 50.93 449 462 4937 1.982 124.73 76.87 930 51.34 558 568 0.0005351 2.148 124.68 76.87 930 59.98 562 574 5351 2.148 124.68 76.87 940 51.34 565 576 5360 2.152 124.68 76.87 940 50.93 509 580 5364 2.153 124. 95 7^89 1710 51.42 964 987 0.0006784 2.723 124.95 70. «9 1715 51.20 970 992 6645 2.668 124.95 76.89 1740 51.25 979 * 1000 6843 2.747 124.96 76.98 2370 51.27 1206 1214 0.0008013 3.217 124.96 76.98 2370 51.17 1207 1214 8028 3.223 124.95 76.98 2370 51,25 1207 1210 8017 8.218 The results in Table 86 justify the predictions made. Compared amongst themselves the values are excellent. Below 1,000^ the data lie below the function {l+a0")iy whereas the extreme points (1,2150) (923) 270 MEASUREMENT OF HIGH TEMPEBATUEE8. [bull. 54. coincide with (l+a6")i almost perfectly. In general therefore the re- sults of earlier investigations (Table 81-85) are emphatically corrobo- rated. HavLDg finished the measurements for air, I passed hydrogen through the same apparatus. The results, near 1,000^ (Table 87), coin- cide almost perfectly with the curve (1 + ad^')i. The results above l,200o are abnormally high, because platinum is pervious to hydrogen. I was not a little surprised therefore on finding the results ac 500^, although very good when compared amongst themselves, much too large to ac- cord with the other data. The error is larger than can be referred to anything short of an undiscovered accident. I suspect the hydrogen of these experiments in some unforeseen way tohaVe been contaminated with either air or moisture, since the error is constant for all the obser- vations. Not being able to discover the cause of the discrepancy, howeveri I resolved to repeat the work with the apparatus adjusted anew. These results are given in Table 88. The results agree much more closely with the exponential (1-f a^')J, showing the corresponding data of the former series in error. The somewhat high values of F(^') are the re- sult of the low value of ;^, to which these data are referred. The diflQ- culties met with in operating with hydrogen induced me to investigate another series for air, which series is given in the last table, 89. The results fall slightly above (l+a^')§ at 500°; slightly below the expo- nential at 1,000°; above it at 1,200°; but the accordance throughout is satisfactory. (See Fig. 48.) The large number of data for Si and ^2, which the Tables 86-89 con- tain, show that the thermal discrepancy has been reduced to low limits, and that its effect is apt to be relatively large in case of low values of 0, To properly jacket the helix is a practical problem of great diffi- culty, because accidental bending or twisting of the thin capillary tube is apt to produce fine longitudinal fissures, or variations of bore, or to introduce other sources of uncertainty or error. Mica insulations be- come friable and can not be thoroughly relied upon after prolonged heating. Hence all the manipulations must be effected with great care, and therefore consume much time. For these reasons I believe that to improve the results further it will be expedient to introduce a radical change of method, such as I will describe below. As a whole, the above tables conclusively indicate that many residual errors are the resultof variations in the composition of the gases. Hence, before proceeding to a general discussion of the above data, I shall in- sert a tabular view of the successive values of the viscosity of the gases at zero degrees centigrade. This is given in Table 90, in which the temperatures d, at which the quantities V 1+4 (924) BAKUB.J VISCOSITY OF GASES. 271 were fonnd, are inserted, as well as the correspoDding valaes of Vfi i+*i computed for them by nsing Holman's equation, V^L =1 +0.002751 e-.0.00000034/9». I also insert the pressure P, at which the gas enters the platinum capillary. Tadlb 90. — Successive values of 170. Gas. III.., Hi ... Hi... Hi.. Air.. Air . Air.. Air.. Air.. Air.. Air.. Air.. H,... Hi... n,... Hi... H) . , Hi. Hi. Hi. Hi. Hi. H,. Air. Air. Air. Air. Air. Date. March 26 March 23 March 21 March 20 March 28 March 20 ...do March 10 March 18 ...do March 15 March 14 .. do March 13 ..do March 10 ...do March 9 March 8 ...do ...do ...do March 7 .do March 3 ..do ...do 7 8 8 8 7 8 7 6 5 5 5 5 5 5 8 8 7 7 7 6 8 8 8 6 8 8 8 1+4 xlO« 133.3 180.4 132.3 132.8 254.8 264.7 252.0 251.2 250.0 250.2 251.4 251.2 144.9 144.2 142.8 143.1 142.7 142.5 141.6 14L8 141.8 140.4 147.8 254.8 282.5 256.5 280.7 257.7 '»• xlO« l+4| P 130.8 123.3 127.5 125.1 129.4 122.2 129.7 122.5 250.0 125.5 249.2 123.4 248.1 124.0 247.2 125.3 248.5 123.1 246.7 123.4 247.9 125.2 247.7 125.1 142.9 124.8 142.2 124.0 140.4 124.0 140.9 123.8 140.0 125.0 139.8 125.4 138.8 128.3 139.8 125.0 148.4 88.7 138.2 124.8 145.8 88.8 250.8 124.5 25a6 88.3 251.5 124.2 258.5 88.5 253.5 124.7 Mean ifo x 10* Hi . . . 129.4 Air . . . 24ai Air . . . 247.2 H, . . . 141.8 Hi . . . 139.6 (Hi . . . 148.0) Hi . . . 138.9 Air . . . 250.8 (Air.. . . 258.5) Air... 252.6 DISCUSSION. Viscosity at zero. — It is expedient to begin this paragraph with an examination of the consecutive values of the zero- viscosity ^0 of the sev- eral gases« since the constant 7/0 must enter fundamentally into all the (926) 272 MEASUKEMENT OF HIGH TEMPERATUKES. [uvLL.ii. inferences to be drawn! Turning to Table 90, on page 271, the singularly high values there incorporated at once strike the eye. The clue to these large discrepancies is, however, at hand ; for _'^\^'^ h) F'--p' t JB* "^^ IB J~VT and it is therefore clear that since — ^ = 4 -p- even slight errors in JB at once produce serious effect on rj. I have stated that because of the dif- ficulty encountered in constructing the capillary apparatus faultlessly, I did not wish to subject the tubes to Any experiment which might tend to injure them ; I stated also that in the discussions of the present part of the chapter absolute data were of inferior interest. Hence, without forgetting the occurrence of the uniformly large values of 7 here found, the question may be waived, to be resumed in the next part in con- nection with other relevant data. The one property of 1^ which has an imi)ortant bearing on the present discussion is its degree of constancy as regards time. If the values of rjo in Table 90 be graphically con- structed as they vary with the data belonging to each, the curves re- sulting show that ffo has a slight tendency to increase. Disregarding 1 be data between March 3 and March 7, which refer to an earlier form of apparatus, it appears that in the hydrogen data between March 8 nnd March 14 the mean increase of 70 ^^ somewhat less than 0.5 per <;eut. per day of use; in the results for air between March 15 and March 26 less than 0.2 per cent, per day of use ; in the final results for h^'drogen between March 20 and 26 the results vary irregularly, and their mean ascent is zero. These data constitute an exceedingly favor- able verdict relative to the pyrometric application of the principle of viscosity. They show that for large mercury pressures like 125"* and 76*="*, respectively, at the two ends of the platinum capillary tube, no serious change of the radius of the tube need be apprehended at tem- peratures even as high as 1,400^ (white heat). In this respect the pres- ent results are valuable. The slight tendency of 7/0 to increase just mentioned, is in accordance with an increase of the capillary radius re- sulting from the excess of internal pressure. This follows from Meyer's equation, but whether the observed result may not be equally weU ex- plained as resulting from variations in the composition of the gases or from similar progressive causes can not be ascertained. It suffices for the present purposes that the time variations of 70 have been found negligible, and that therefore the dimension of the platinum capillaries used in the above experiments have remained practically unchanged, when the mean excess of internal pressure at white heat was about ^ of an atmosphere. The use of different gases (air, hydrogen) in these experiments was principally to vary the conditions of experiment au4 to detect the laws (926) BARU8.1. VISCOSITY OP GASES. 273 of variation with greater certainty. Hence ordinary care was taken in drying the gases, air being passed through a tube of GaGl2 and hydro- gen both through OaCls and concentrated H2SO4. But neither was the hydrogen purified of sulphide or air or other attendant gases, nor was air purified of carbon dioxide. I desisted from these special pre- cautions because above red heat platinum is pervious to the hydrogen gases of the Bunsen flame, so that in non-euameled platinum capillaries the purity of the transpiring gas could not be vouched for, even in the case of a gas originally pure. Again, at the temperatures (500^ to 1,300^) within which my data chiefly ai)ply slightly moist air and dry air, pure and gaseously impure hydrogen, are probably equally perfect gases. Hence there occur in my results two values for the zero-viscosity of hydrogen, 140: 10^ and 129: 10^, respectively, which correspond to gases taken from different gasometers at different times. The variations of ^0 for air are smaller, ranging from 247 : 10^ to 252: 10®. The variable character of th made it necessary to make the low-temperature measure- ment before and after each series of high-temperature measurement made. Indeed, I did not anticipate such large fluctuations in 7^, and despite the precautions taken the discrepancies here in question have produced no trifling distortions in the high temperature results which follow. This I shall soon have occasion to show. When the gases forced through the capillaries are urged forward by an advancing sur- face of mercury (as in the above experiments) traces of mercury vapor will also pass along with the gas, but the tension of mercuiy vapor at 209 is only 0.002'^'° to 0.004*^'°. Hence this discrepancy is nil. Finally, Table 90 contains values for 7/0 derived both for P= 125*^™ and for P=88*^»". Curiously enougli, the value of rf^ for low pressures (P) is decidedly the greater, being about 5 per cent, greater for hydrogen and about 2 i>er cent, greater for air. This result belongs also to the dis- cussion of the next section. Here it is sufficient to note that if meas- urements were made at smaller values of P than the ones customary rr" (126*"»), the relative values — where ;/' is a high-temperature viscosity, would not be larger in value than those admitted into the above tables. In other words, so far as the present evidence goes, the zero-viscosity Wo has not been increased by the relatively large values of P (125°"*) em- rf' ployed throughout the course of the work, and hence — can not be too small. ViHcosity at high temperatures^ kinetic inferences. — In order to pro- ceed with the discussion of the high-temperature viscosities. Tables 83 to 89 may be consulted, the values of Tables 81 and 82 being in error in the sense already indicated. If all the values of F($") be constructed as functions of ^', the graphic representation Fig. 48 will show that the individual data group themselves in a baud or pathway, of which the function (l-^aO") is so nearly the axis that it is at once justifiable to ^lyiept it as such. Hence, even if there were no ulterior reaaow^tot^R*- Bull. 54 18 (927^ Il 274 MEASUKEMENT OF HIGH TEMPERATURES. jsuLuiL ceptiQg the given function, it is, at tbc present stage of investigation, a justifiable inference that the viscosity of a perfect gas varies as the § power of absolute temperature. Kow, inasmuch as by the relation of Maxwell 7=0.318 pLHj where p is the density, i2 the velocity of the mean square, and L the mean free path of the molecule of gas, and inasmuch as.Q=/2o Vl+aS" and L are the only variables in this equation whose values change with ^', it follows that i=Zo y/l+a6" In other words, the mean free path of the molecule of a perfect gas varies as the sixth root of absolute temperature. Moreover, in view of the equation /2=/2o Vl+a^', it furthermore follows that the mean free path of the molecule of a perfect gas varies as the cube root of the velocity of the mean square. This re.sult is suggestive, perhaps ; for if there be given a gas consisting of a fixed number of molecules in a fixed volume, or, in other words, if p be constant, then the only effect produced by varying the temperature 6*' is a mean increase of X2 dis- tributed uniformly throughout the volume of the gas. If the change ofJCl due to temperature be taken as a measure of the e£Fect produced by temperature, as it were equally in all directions, then the part of this thermal effect apportioned to the linear magnitude L is plaasibly represented by the cube root of /2. Again, if the equation of Glausius be considered, viz, X- — — where P is the mean volume per molecule and s the radius of Olaasins's " Wirkungssphiire," then it appears that the volume inclosed within the " Wirkungsphare^ is diminished in magnitude by temperatare; and that the diminution takes place proportionally to the square root of the velocity of the mean square (/2). Sources of error.— Having thus stated the general character of the results of the above tables, it is necessary to find the conditions upon which their validity depends, and to inquire as fully as the present re- searches permit into the facts which militate against the inferences . drawn. This is by no means easy, nor even fully possible on the basis of the experimental material in hand. The principal cause of discrepancy in the present work is this, that even in the most carefully a^usted forms of the present apparatus the meaa BABU^J VISCOSITY OP GASES. 275 temperature registered by the thermocouple aud the mean temperature of the helix of capillary tube are not necessarily the same. Each of tbe«e pyrometers furnishes its own thermal datum correctly ; but these data have reference to environments which are not thermally identical. In short, the degree of constant temperature throughout the space en- . veloping the helix is as yet far from satisfactory; and the residual differences of temperature between the inside and the outside of the helix or between its top and bottom surfaces have not been rigorously allowed for. To this must be added the fact that the thermo-couple was not compared with the air thermometer at temperatures above 1,300<=^, and that the calibration in question loses in accuracy when • these high temperaturesAre approached. (Cf., Figs. 41 and 42.) Hence^ in view of the great difficulties in the way of correct temperature meas- urement, it is hardly profitable to enter into more than a cursory con- sideration of the minor sources of error. In addition to the extraneous causes for incorrect temperature meas- urement, there is also an internal cause, due to the expansion of the transpiring gas from the pressure P to the pressure |>. Meyer has elaborately discussed this phenomenon, ^gain, the purely convective effect due to the introduction of cold gases into the capillary tube is not to be lost sight of. In experiments of the next section I found a cool- ing effect as high as 20^. In tile present experiments, where thin tubes and slow currents alone occur, the convection error is nil. To avoid incidental complications the radius of tiie capillary tubes here in question was chosen small {R <0.01<=™), so that the Meyer for- mula fully applies. Again, preference is given to absolute methods of experiment; differential methods, inasmuch as they compare two mag- nitudes without fully characterizing either, would have encumbered the present research with an additional element of uncertainty. Diffusion, — ^The observed circumflexion of the curve which repre- sents the mean distribution of the points in the diagram, Fig. 48, at a temperature near l,000o, together with the fact that this change of the sign of curvature is much more pronounced for hydrogen than for air, points, I think significantly, to the occurrence of diffusion of gases through the walls of the platinum capillary tube. In the case of trans- piration experiments with air, the hydrogen gases of the burner passing through the platinum septum combine with the oxygen of the capillary current within. There results an increase of the volume of the oxygen combined as 1 : 2; but as the water formed is absorbed in the pneu- matic apparatus, it follows that the volume Fo actually measured by the burette is too small. Again, in the case of transpiration experi- ■ ments with hydrogen the prevailing diffusion is from within outward, so that hydrogen simply leaks out of the tube. Thus the volume of Vq actually measured is a^ain too small. Hence in the case both of air and of hydrogen, since Vq is negatively in error, the error of r/', which varies inversely as Fi, will be positive. This accounts Cot tVi^^ ^Vx^xwac- ^929) 276 MEASUREMENT OF HIGH TEMPERATURES [bull.M. flexion discrepancy inquestion, or at least for tlie difference of behavior of hydrogen and air. A final remark relative to the surface disintegration (Zerstaubang) of red hot platinam, as observed by Nahrwold^ Berliner*, Kayser^, and others, inust be made here. Unfortunately my work was too far ad- vanced when this phenomenon^ was being discussed to permit mo to- make special investigations with reference to it; nor do I now see how allowance for the phenomenon is to be made. I do not believe that the error thus left unaccounted for is of a serious kind. For instance, in NahrwoldV last paper it is shown that metallic particles fly off from . red hot platinum much less easily in h^'drogen than in air.^ In case «)f both gases, however, the thermal relations of viscosity are subject to the same law. Hence the discrepancy due to surface disintegration is . probably nil. 1889. Sliding coeffieienU^-To return to the formula selected on page 273, it appears from the remarks there made that the fuU form in which it applies to transpiration work must be '^' - '^° (1+a^'O* «/^- ^^^Eo i+pe" ^^^Ro where -Bo is the zero radius and ft the mean coefficient of expansion of the platinum capillary through which transpiration takes place. This formula, follows at once for the law accepted above (r/'=;;o(l+o'^)§), and from the fact that C9 which is Helmholtz's Gleitungs coefficient, has been proved by Meyer, Kundt, Warburg, and others to vary proportion ally to the mean free path. It is usual to take as a quantity negligible in comparison with 1. If this be permissible, then will Co 'y/i+ad'^ ^Ro l+>/y'' within the limits of the present interval of temperatures also be negli gible. For the coefficient 1 Nahrwold: Wied. Ann., vol. :U, lrt87, p. 473; vol. 35, p. 120, 1^88. « Berliner: Wied. Aun., vol. 33, 1888, p. iM9. 3 Kayser: Wied. Ann., vol. 34, l^-**^, p. 007. * Prof. Cleveland Abbe kindly called my attoniion to it. ahrwold: Wied. Ann., vol. 35, 1888, p. 120. ElBter u. Geitel: Wied. Ann., vol. 31, 1887, p. 109. (930) BARUB.1 VtSCOSttt OF GAStS. ^11 at 500O, 1,00(P, 1,6000, is not greater than 1.15, 1.22, 1.23, respectively, whereas its probable maximam is reached at an earlier temperature. Hence, if the views maintained at the present stage of molecular kinetics be indeed correct, then no effect of the thermal variation of the coefficient of external friction need in the present work be appre- hended. This is an important inference, for it mi^ht easily be sup- posed that the relation which Holman found to hold between 0^ and 100^ r^'=l+0.002751 1— 0.00000034 f ^ might be progressively retarded in proportion as high temperatures are reached, by the gradually increasing values of 0+4) and in this way lead to the results which I have found. Advantages of an exponential laic. — It is next desirable to examine into the reasons in virtue of which, at the present stage of research, the equation f/=fjQ (l+ar^")f may be accepted preferably to any other form. I will state here, inasmuch as one of the chief purposes of the present investigation is the introduction of a new instrument of high- t«*mperature measurement, that any exponential form (l+aO^*)^ which is in good accordance with the observations in hand is particularly, acceptable, because it facilitates the calculation of thermal data by the principle of viscosity. Hence, when the choice is open between a num- ber of equations, apparently of equal availability, the exponential form will always be adopted, because of the practical advantages just stated. Strictly speaking, the formula accepted for ?/' (r/'=//o(l+a^")*) is applicable to the case of a diatomic gas. In the case of monatomic gases, the supposition that the atoms are hard elastic solids leads to the law ;;"= y/l+ad^\ as Maxwell and Meyer have elaborately shown.* From this law Maxwell* was led to depart, after having made a series of* experiments in which viscosity appeared to vary directly as the absolute temperature of the gas. Maxwell thereupon deduced a law of repulsion between the molecules of a gas varying inversely as the fifth power of the distance between them, an acceptation by which his equations were capable of much simplification. Inasmuch as all the subsequent experiments made by many observers have failed to confirm Maxwell's experiments, it appears from this and from other evidence which Meyer^ adduces that Maxwell's law of fifth i)owers is untenable. No other law of repulsion between molecules having 1 Maxwell: Phil. Mag. (4), vol. 19, 1860, p. 31; Moyer: Pogg. Anu., vol. 12r», 1865, pp. 177, 401, 564. 'Maxwell: Phil. Trans., I, p. 249, 1866. »Cf. Maxwell: Phil. Mag. (4), vol. 35, 1868, pp. 129, 185. Meyer; Kinetische The- orie der Gase, $ 77. (931) 2?8 MEASUREMENT OF HIGH TEMPEBATUHEB. (bdll.61 since been proposed, the question regarding the thermal variations of viscosity which depends on the said law remains theoretically un- solved. Hence, between forms of an equation for rf' as a function of temperature, it is permissible to select the one among many applica- ble forms which confers the greatest practical advantage. In the present instance (to give an example bearing on the remarks just made) there is another form of equation which, besides its inherent simplicity, might be applied to reproduce the observations in hand. Tliis is 7/'=;7o (l+;^^0 ( Vl+a^Oi which means that li=io (l+y^')j »"V-^ (^+^-0064 6) . . (14 (035) 282 MEASUREMBNT OF HIGH TEMPERATURES. [Buix.5i. a form which also ioclades eqaation (12), since A and B are constants. In the case of any instrument the capillary bore of which is variable along the length of the tnbe, or which can not be determined, A and B may be found by exposing the viscosity pyrometer to two known tem- peratures. For greater accuracy such an instrument may be directly compared with the air thermometer in the way soon to be indicated. In this place it is pertinent to call to mind certain valuable properties of the explicit equations (12) and (13). In the first place it is clear, inasmuch as the right-hand member of the equations varies as the \ power of absolute temperature, that the transpiration thermometer is unusually sensitive to variations of temperature. Again it appears that the one consideration in which the equations might seem to be of^ questionable applicancy, viz, the occurrence of the fourth power of (1-f >3^0> becomes of less serious moment because this expression only effects 1+a ff' in the 2.4 power of (1+/^^')* Hence the coeflScient of thermal expansion ol platinum, it known with an accuracy of only 10 per cent.,would not affect the result more than 0.2 per cent, at 1,000^. Furthermore, in the case of known fixed thermal data, like those dis- cussed in Chapter II, /? may be directly determined from transpiration measurements made with the instrument itself. For it is merely neces- sary to solve equation (14) with respect to /3 in order to determine this constant with the same degree of accuracy with which it is to be used. Finally the quantity B. 4 ^0 which enters into equations (12) and (13) can also be directly determined from measurements made at the low temperature. For, disregarding the unessential correction members, equation (5), on page 253 shows at once that in which if the measurements are made at 0, tj may be reduced to i^o by Holman's coefficient. With this operation the fiducial zero of the vis- cosity apparatus may be said to be determined. -Bo*/'?© is more ac- curately determinable in this way than by gravimetric measurement of B. Besults, — To give emphasis to the remarks on the probable excellence of the viscosity pyrometer, I will use the data in Tables 86 to 89 for the calculation of temperatures from data based on the viscosity of the gases operated with. In Table 92, 0^' denotes the temperature, thermoelectrically measured, at the points of the helix shown in the diagram, Fig. 47a. [6'*] Is the corresixindiug datum of the transpiration pyrometer. (930) BARU8.] VISCOSITY OP GASEa 283 Table 02. — Temperatures measured thermO'eleetrically and by the transpiration pyrometer. Air S" [fl^'l Diff. • B" [9"] Diflf. ,„ . + 2 520 511 + 9 Hydrogen. 958 956 662 540 +13 960 058 . + 2 667 558 + 9 962 059 + 3 586 672 +H 962 960 + 2 598 583 +15 970 975 - 5 Air 094 964 +30 Hydrogen. 1209 1329 -120* 094 963 +31 1212 1338 -126 996 966 +30 1215 1337 -122 Air 1212 1217 - 5 Hydrogen. 414 434 - 20 1217 1227 -10 416 437 - 21 1219 1222 - 3 421 441 - 20 Air 1 430 442 -12 423 445 - 22 436 450 -14 Hydrogen. 607 529 - 22 446 458 -14 513 535 + 22 455 467 -12 515 518 53G 541 - 21 - 23 Air 563 571 - 8 620 543 - 23 568 574 - 6 521 543 - 22 5T0 575 577 580 - 7 - 5 Hydrogen. 946 952 963 908 - 17 - 16 Air 075 965 +10 954 974 - 20 981 971 +10 955 976 - 21 990 981 + » Air 1209 1210 1210 1245 1245 1247 -36 -35 -37 * Platinmn peryions to hydrogen. The errors of this table are apparently large in places ; bat they ar^ by no means excessive when the great difficulties of experiment are justly taken into account. The observation of especial importance here is that the distribution of errors is promiscuous. A difference of 125<=^ occurs m the case of hydrogen transpiring at 1,20(P; but at this tem- perature platinum is seriously pervious to hydrogen. In some measure the errors are due to the fact that the gases referred to the same t^ were not absolutely identical in composition. This is particularly the case in the final data for hydrogen in which the nearly constant error —20^ is due to the erroneously low tjo here inserted — as I have already pointed out, page 271. Beyond this I believe that the differences of temperature remaining indicate actual differences of thermal environ- ment for the two thermometers here compared. They show that throughout the space enveloping the two pyrometers temperature was not rigorously constant, and it is quit'C in keeping with the present method of experiment to suppose that the mean temperature, 6'\ of three points as given by the thermoelement, and the mean temperature [^''J, for the length of nearly G?*" of platinum capillary tube, will not even in (937) 284 MEASUREMEi^T 01* HIGit TEMI^ERATUEfiS. [bvvl.5L the final experiment have been identical within 20^ at 1,00(P. Taking the transpiration data alone they manifest a striking degree of accord- ance even above 1,300^, a8 may be readily proved by the earlier tables, 81 to 85. Again the uniformity of variation of a given thermal datum, whether measured thermo-electrically or by the transpiration pyrome- ter, proves beyond a doubt that high thermal data are measurable at 1,00(P in terms of the viscosity in gases with an accuracy of a few tenths of a degree. TRANSPIRATION NOT SUBJECT TO THE POISEUILLE-METBR LAW. Objects of the investigation, — ^The chief difficulty in operating with capil- lary tubes of a bore so fine that Meyer's formula is rigorously applicable at low temperatures as well as at high temperatures lies in the fact that thcf fiow in such tubes almost ceases when the degrees of white heat are approached. There are a number of ways of obviating this annoy- ance, in the first of which fascicles of tubes are used side by side; in the second of which the transpiring volumes are measured in graded apparatus, so that at high temperatures small volumes may be measured as accurately as large volumes at low temperatures. Again, transpira- tion may be allowed to take place through graded capillary tubes of platinum the length or bore of which increases by some given law; or with the slow current in continuous flow, rates of transpiration i'v) may be measured by some applicable method of repetition. It is nevertheless desirable, however well these means suffice for the attainment of the end in question, tx) try to arrive at practical results relative to tubes of a bore so large that Meyer's formula is no longer applicable. All these endeavors are decidedly in the interest of expeditious work, for I find that compared with each other such meas- urements are not lacking in accuracy, although the total time consumed for observation may not exceed a minute. To make these observations greater volumes of air are necessary. Hence 1 have found it desirable to measure the volumes before they enter the platinum capillary tube. I mention this here to point out an important peculiarity of the above apparatus. It is easily possible so io adjust it that the gas may be measured both before entering and after leaving the platinum capillary. The observer then has it in his power not only to detect the presence of gross leaks in the apparatus with certainty, but to follow the gas in its motions either (normally) through the capillary canal or (by diffusion) through the white-hot walls of platinum tube.' Moreover, it will be noted that the experiment in gaseous flow through capillary tubes are accompanied by something re- motely similar to self-induction on opening and on closing the circuit. For when the stop cock ii in Fig. 41 is opened, the air rushes in the dead space » See remarks relative to impure bydrogeD| p. 275. (938) BARisl VISCOSITY OP GASES. 285 • between stopcock and capillary tnbe antil the high pressurePis reached; and after closing the stop-cock the compressed air of the dead space is gradually discharged. The method of eliminating the positive error which is thus added to the transpiration volume ( Vq) has been indicated on page 257. But when the transpiration volume has to be chosen small the dead space discrepancy is more serious in character even when re- duced to the smallest value compatible with the practical efficiency of the apparatus. These difficulties are quite avoided by using tubes of large bore and larger volumes of gas, and hence a second reason why the experiments of the present paragraph are desirable. HoffmanrCH researches, — From a theoretical point of view^ the con- siderations involved are, of course, of extreme difficulty and compli- cated in mathematical character. As such they must be here omitted. From an experimental point of view, the difficulties encountered are fortunately less formidable, and an excellent analysis of the subject, based on a variety of observations, has been published by HoflFmann.* Hoffmann, after recognizing that the chief discrepancy is introduced at the ends of the tubes, derives his first eq uation by successively ap- plying Navier's equation vp=R^ n 7Cx rsj ClnV): for the ends of his tubes, and the PoisenilleMeyer equation for the intermediate parts. Unfortunately, even in the favorable case of slight variation from Poisenille-Meyer's law, this process leads to very involved results : _J^7tdg (Ttx ^ - 712^) ^1 = VJM — 16;^ jPi{l- 2 (vpY _ 2{vpf (t>p)« 7t2=p2e^^^, where |>i and pz are the observed pressures just before entering and leaving the capillary tube, and tti and ;r2 are the corresponding press- , ures in the first and final section; 0=-^^'^^ ^L"^^^ and the remain- ing variables have a meaning which is easily understood from the discussion on page 253. 7r=3.1416 and e is the basis of the Naperian »The literature is digested by HofTuianD (i.e.) as follows: Navier: M^m. de TAcad. de sc. de Paris, vol. (J, 1823, p. 389 ; PoissoD : Journale de P^cole Polyt«chnique, vol. 13, 1831, p. 139; Stokes: Trans. Cambridgo Philos. Soc., vol. 8, 1849, p. 287; Cauchy: Exerc. do Math^m., vol. 3, 1828, p. 18:^; de St. Venant : C. R., vol. 17, 1843, p. 1240; Stefan : Wi«n. Ber., vol. 46 (2), 1862, p. 8. 'Hofifmann: Wiedemann, Annalen Physik, new aeries, vol. 21, 1884, p. 470, (939) 286 MEASUREMENT OF HIGU TEMPERATURES. [bull. 51. • logarithms. Unfortunately these valaes of tt^ and ;ra themselves con- tain t!p, for which, however, the approximate value given by Poisenille- Meyer's law may nsnally be substituted with sufficient accuracy* In view of these difficulties Hoffmann investigates an empirical rela* tion by observing that (cseteris paribus) the certain small len^h of maximum efflux is subject to Navier's law, whereas as length increases the efflux obeys Poiseuille-Meyer^s law. If, therefore, time of efflux (ca3teris paribus) be studied as a function of length, Navier^s law fixes a point, while Poiseuille-Meyer's law fixes an oblique line passing through the origin. Hoffmann then supposes on the basis of his experi- mental results that the actual passage from the point te the line takes place nearly along an hyperbola, of which the said point is the vertex and the said line the asymptote. A suitable modification of this hy- pothesis leads Ho£Fmann to the equation vp=z ri~"7T {Nioby where ^^ l^tfl jf^^]^£(Pi+P2) r~C , 2pT ^"" 2 V 0.43429 ^l>,+i>2 and where b=:{l+i) (2 2+4) and a has a tabulated value of nearly 1, but varying with the mean diflference of pressure. Hofifmann's equation contains difficulties of calculation of a very tedious and impracticable, kind, particularly in view of the involved occurrence of the factor (7, which represents the thermal variations of the transpiring gas. With full deference, therefore, for the accu- racy of application which Hoffmann has reached in his results, I shall nevertheless compute 77 by the formula (5) on page 253, above; 1. e^ directly by the Poisenille-Meyer law. Having done this, it was my further object to find from the known law of variation of 77 with tem- perature, what correction was to be applied to the Poiseuille-Meyer equation, to make the data for tubes not rigorously capillary conform with the data already in hand for truly capillary tubes. The plan which I have in mind is somewhat different from that of Hoffmann and more in harmony with the general tenor of my experiments. The form which I aim to give my correction is an exponential, in which the dimension of the capillary tube and the actual viscosity of the transpiring gas are the variables. I found, however, that to do this satisfactorily it would be necessary to repeat my experiments at greater length than I am now justified in doing; and observing that the data which I have in hand make up a diagram of the transpiration phe- (940) BABUB.1 VISCOSITY OF OASES. 287 nomenou ia wide tabes, of remarkable clearness and fall of snggestion, I resolved to commanicate these withoat elaborate reductions. EXEBIMENTAL BESULTS. • Transpiration under variable pressure F-^p, — I shall introdace these results by a number of experiments made at the outset of the present investigation, inasmuch as these have a direct bearing on the feasibility of the transpiration apparatus for pyrometric purposes. In these ex- periments neither Mariotte flask nor lateral lube was employed, so that the pressure fell from the initial to the final value at one end of the tube, the other being at atmospheric pressure. The helix itself was wound in a flat form of large radius so as to lie completely in the zone of fusion of the Bunsen burner. For each special part of the table the conditions of flow, however complex, are the same, t is the time of efiiux of the volume T; L and { denote the length of tube and cold ends; R is the internal radius. In Table 95 the tempestuous influx of mercurj' into the receiver B was avoided by opening the stop-cock of the Mariotte flask until the flow of mercury had ceased, and then open- ing the stopcock of the capillary. Table 93. — Transpiration of air under variable pressure, {Burner not ohimneifed,) [Capillar^' tube No. 1. L=2n*^. J=8«". if=0.02y». Fo=5«)«'. 9=7fP.] Time. i Initial pressure. Final pressure. 1 Barome- ter. Temperature. 1 98 ) ' 20^. 469 Bright rod heat (1,000°). 99 108 97 78 > 20O. 459 Bright rod heat. 98 ■ • 20°. 78 ■ r 20O. 323 Bright red heat. 78 118 107 78 i 20°, 814 Bright red heat 7d t 2a3. 189 \ ' Bright red heat. 67 20O. 187 > 143 132 78. Bright re41) MEASUREMENT OF HIGH TEMPERATUBE8. Tabls 94. — Transpiration of air under variable prMntre. ( CAimnojwf ixmer.^ IPUWnoin cspUlary mbo Mo. I. i=l7™. J=i™. Ji=0.(l»ra-. 7'„=5§((".1 Time. InltlKl Final ™:, 1»>. MB I 118 n. 78 1 Bright rod b<*l. tS2 Brigbtredbwt. J*6 . ( 18". HW W •1 78 J Brl|ihtn = 76.96. BARUB.] VISCOSITY OP GASES. 291 Tablk 98. — Apparent viwotity of air at Jtigh temperatures. Absolute measurement. ICapOlary tube Ko. S. X=42'-. I=4». ie=O.O20». F^JMO^. 9=5^. ThermcMsoaple No. 37.] p P-p f* ^•-l>*xt" P 0" n" r 1+4 ^"/JK" •87.6 11.8 212 6120 o 5 0.000270 l&O 01.9 15.6 160 5480 5 200 18.0 97.0 20.7 127 6050 5 826 18.2 102.2 25.9 106 6410 5 . 351 18.6 107.6 81.3 91 6850 5 875 1&2 112.0 35.7 81 7120 5 380 18.2 117.1 40.8 73 7540 5 410 If 5 t88.3 U.3 220 5300 14 0.000285 93.2 16.2 162 5800 14 300 98.2 21.2 128 6158 14 828 •••••••• 103.2 26.2 106 6498 14 846 •••••••• 108.3 81.3 92 6030 14 860 113.5 36.5 81 7315 14 880 •••••••• t80.6 12.8 269 7460 100 0.000312 16.5 017 17.9 201 8030 100 386 16.5 100.5 28.7 156 8530 100 357 16.6 §92.0 15.0 1209 89800 041 6.000562 98.9 21.9 796 89740 041 560 105.7 28.7 585 30840 034 564 112.7 85.7 463 39840 033 564 *•*— p=76.8. fi>=77.0. :p=76.8. §i>=77.0. TaBLB 99. — Apparent viscosity of air at high temperatures. Absolute measurement. ICapilUry tnbo No. 4. Z'+«"*=4—. i=42.5«. F=56e«-. Jl=0.025«». •=4^'. Thermo^ioaple Na 37.J p P-p r P •" n" 1+4 <"/^" •8&4 0.6 268 5300 o 0.000266 22 86.4 0.5 267 6400 267 22 80.7 12.8 204 6600 281 22 00.2 13.3 200 5780 285 21 00.8 13.0 104 5870 280 21 01.2 14.3 189 5020 292 21 06.5 10.6 146 6480 310 21 06.6 19.7 147 6630 321 21 101.6 24.7 121 6080 845 21 101.8 24.0 121 7010 345 21 106.0 30.0 104 7450 0.000368 22 107.0 30.1 103 7420 366 22 111.3 84.4 02 7750 385 21 112.2 35.3 00 7830 886 21 112.3 35.4 00 7840 882 21 115.1 3&2 85 8100 403 22 117.3 40.4 80 8170 400 22 tf8.0 12.0 1000 25850 636 a000428 10 80.0 12.1 1023 26850 658 435 10 123.7 46.8 260 31780 652 514 10 123.6 46.7 263 82060 658 516 10 05.8 l&O 665 28360 684 446 10 C945) 232 MEASUREMENT OF UIOH TEMPEEATUEEB. [bi-u-BI. TABLX^S.—Apparmtriiaifiljio/alrathiffk Imperatura. Ah*oUt«mea»»Tement—Coal'i. p r-p "r. p oos l+4("'«" tio I&T Wl 28070 447 20 3V.S te: 407 Ilfl.J SB. 8 317 S18I0 «M U« m IM-l 2U.2 20010 18T tSB iM.a 21). 3 434 3033Q on n IJ3.7 SOU S27W tM Sll 123.7 48.8 see 3i70n 687 Sll 31 ;m.2 18.0 m 2D01W m D.OOMSI so BS.J 1&8 724 vmo 744 4B7 20 9S.3 7ST a2»io 78B 12S.( «. 1 3US 37S4U wa m 11 Sll araw MR OS,: IB. 8 835 a.usu SSS 4» IB K.< 847 38S10 123.2 40.9 XT lOlM SIR KM 10 40340 804 06.4 111.1 804 87270 OT8 4B4 10 4123. S ■ 47.3 «B 44gtO M8 O.OOOSU SI 4S5iO BM S4g 21 sa.2 12.0 irai 44440 M8 SST S 88.^4 44320 1004 sa 13 is.e 47.4 MO 4S50D lOOS S4S M (5770 lOOB S40 88.3 1=1 loss 442M 1004 S.TS S4 •(.=70.0. tp=7«.S; ;p=78.J. 4p=7<.E. Tablk 100.— Jjiporcnt HtMuify o/ air at high temprratnres. Abnolute meaturei ICipHIiiiT tiilw No. 5, £=35.1. ft=«.02J'-. r=505.7". t-T. P+r"=J.O~-l p •123.81 40.70 J-_ 5r- 63200 »" l+n>' . 12SB 0.000585 10.1 124. TO 47.73 420 03260 1280 6SS 10. s 1280 10 8 80.20 laio 1012 00840 ISM SOS 21.0 MWO 1207 S«7 22.0 1124.01 47.01 423 02700 1300 670 22.1 1S4.B7 47.07 42! 52000 1305 578 22.4 :121.24 4-. 31 B37 41000 1048 0.OO0.-i4l 22.8 41«30 104S 22.B 88,00 11-07 1408 87810 1M4 405 22.G 88.00 37020 1043 21.8 124.31 47.38 334 4130O io;>5 S40 22.0 la.ii 47 :k 334 41170 103S S3R 22.0 5108.44 31. H 02 7008 T, 0.000380 22.0 82.22 7016 2J.0 «i,8l 8.08 ^01 4840 273 22.5 ^f.ea 203 4Agl 215 wi.7a 8.03 202 48S1 273 22.6 32.11 0085 30R47 31.02 82 7015 380 22.5 fp=T7.00. :p=Te.03. (946) BA1U8.1 VISCOSITY OP GASES. 293 Among these tables the first is unique, and I shall therefore specially refer to it. The capillary tube used is the same with which the data in Tables 81 to 90 were investigated; but for the large volume Yq the time of efflux at red heat (977o) is five hours. During the whole of this time 6" and P were measured so as to obtain a fair mean result and eliminate unavoidable fluctuations of temperature. It is exceedingly gratifying to observe that the value of F {0*') computed from these observations conforms very well with the data of Tables 81 to 89, and with the law rf*-=TjQ{l+aO'')\ despite the great difference of method of measurement employed. Differences of tf^ in different parts of the table are due to imperfections in the earlier adjustment; but the values of i^b measured before and after the high temperature measurement agree satisfactorily. Variations of //o with P will be discussed below. The negative error of F(d") may also be anticipated, since in so long a period of efflux (five hours) even minute leaks in the compressing appa. , ratus would produce appreciable results. Transpirations compared differentially. — Before proceeding with the discussion of these results it is expedient to communicate the data obtained with a diflerential apparatus. The formula for this method of experimentation has already been given. Hence the results of the following Tables 101 to 103 need but little further elucidation. The ad- justments here are identical in plan with those of the differential gal- vanometer. In Fig. 55, p. 305, air is supposed to enter at a and to pass through the stop-cock K^ where the bifurcation of current is brought about. Supposing K open, a part of the air passes through the hot spiral H and thence to the measuring-tube Vg ; the remainder through the cold helix 0, and thence to the measuring-tube V^. Fh and Fg cor- responding respectively to the temperature ^ and 6" are ^ven in the Tables. If ^=6^", then the results contain data for the computation of the ratio of the radii of the two helices. If ^^> 6^ the results lead to J^i(n= - V" 1 . ^^"' / l+_iV the beauty of the method being this, that time and pressure measure- ments (in the case of capillary tubes of very small bore) are superfluous. I have purposely used tubes of large bore however. From Pi(6^')> V " /C+jI^.) may be calculated by inserting the corresponding values of // from Tables 96 to 100. (947) 294 MEASUREMENT OP HIGH TEMPERATURES. (bull. 54. Table lOL-^IHfferential meaaurement. Apparent vxaoosity of air at high temperaturet. iCapillArytabeMKoB. Sands. I'+I^'sO. I"rr36.1«-. X=36.1«>. J2=0.026^. Couple Na 87. i»=76.3. • «4^.1 p-p n Ti 4 C" I|"(1+-rV» ii/(l-H{/«t) 9" P Bk/Rt 16.7 15.1 1L5 &9 48.51 46.01 48.09 48.44 47.14 62.17 50.43 63.57 5L22 48.06 o 92.1 90.4 86.9 84.3 0.928 0.911 0.914 0.946 0.981 P-p 51.8 60.2 50.7 53.0 48.4 48.6 46.2 45.7 50.2 50.3 50.8 y. 0" P 7.9 11.0 16.2 20.6 25.8 31.1 27.8 23.1 19.2 14.0 9.2 16.5 16.5 ie.9 16.6 18.6 16.7 6.4 15.4 16.9 16.0 14.6 1.30 1.22 1.15 1.18 0.92 0.99 0.06 1.02 1.03 1.10 1.22 454 483 505 531 578 617 620 612 604 694 689 88.4 86.6 CI. 7 96.1 101.8 106.6 103.3 98.6 94.7 89.5 84.7 Table li/2.— Differential mcMurement. Apparent viseoaity of air at high temperaturea. [OjpUlary tabe* Nm. 5 and 6. l'+l"'=5»-. Z"=30.0«. I=36.0««. J?=0.026«. p=76.2. •=94eoj. p-p Fh Fg V'(l+a^') (l+/5«)« 1,(1 + «tf) d-^ffO")* $'* P 48.3 50.54 42. OG L87 (1200) 124.5 12.0 51.95 89.87 L48 88.2 48.2 52.59 44.19 L36 124.4 11.9 5L59 40.26 L46 8&1 11.8 51.09 34.86 1.66 (1300) 88.0 49.3 51.62 37.46 L57 .••••••. 125.5 11.8 40.79 35.76 L58 • 88.0 51.7 52.77 41.30 L45 1160 127.9 12.4 52.69 3a 51 L56 1100 8&6 51.7 50.99 3a 31 1.61 1160 127.9 51. G 52.19 30.20 L63 1280 127.8 12.3 51.87 34.29 hll 1280 8a5 63.0 52.02 • 37.61 L57 1280 129.2 (948) ^ BARUB.] VISCOSITY OF GASES. 295 Table 103. — D^ermitidl meaguremeni. Jjfparent viMoaity of air at high temperutwrtB. (Cspillary tabee Nos. 6 and 6. i'-{-l'"=4«. 2"=ao.4^. JD=il.2<». £=0.0184"-. Thenso-coaple Ko.87. 0s4P.] p-p Ffc y. •" P P Sk/Xt 89.0 10l7 10.7 10. 8 30.9 43.8 44.7 43.3 48.6 44.4 62.5 62.2 51.0 52.1 61.3 117.4 88w8 8&2 8&3 117.3 77.6 77.6 77.6 77.5 77.6 1.00 LOS LOO LOO L04 f P-p Ffc • F{e") •" P P n r i^% 44.0 11.0 44.6 11.7 44.5 44.7 11.7 44.8 11.4 46.2 11.6 61.2 6L0 61.0 52.1 61.3 61.6 62.5 62.1 62.8 61.6 52.4 16.2 12.2 15.4 11.5 14.0 0.64 7.22 0.61 7.05 a40 6.06 1.88 1.78 1.37 1.86 1.40 1.61 2.17 1.68 2.28 1.63 2.24 687 606 614 624 630 073 074 077 077 078 070 121.6 80.4 122.1 88.2 122.0 122.3 80.3 182.4 80.0 122.8 80.1 77.6 77.6 77.6 77.6 77.6 77.6 77.6 77.6 77.6 77.6 77.6 • 0.O00B62 8S0 864 268 863 0.000864 266 864 267 866 868 6.000501 461 498 480 608 0.000687 600 608 674 606 678 It was not my object in this place to carry this method to a high de- gree of perfection, bat rather to show the feasibility of measurements made in this expeditions and simple way. This the tables effectually do. Table 101 shows that for tubes of the large radius i2=0.025<'°' the results ai'e not accurate when so small a volume as FsrSO®^' transpiring at zero, is made the standard of comparison. They are irregular. On the other hand, when the standard volume transpires at high tem- peratures (^=9000 and &">0)j this method proves to be quite feasible and the results regular (Table 102). For tubes of finer bore (jB=0.018«»), Table 103 shows that the data are consistent at all temperatures. Fortunately, in the differential method the errors due to the dead space between stopcock and the capillary, if this space be made small, is nearly eliminated. DISCUSSION. Apparent visoosity and pressnre^ — To obtain a clear insight into the data of these tables, it will be necessary to construct them graphically. This has been done in Fig. 54, p. 304, in which the abscissae are P—pj and the ordinates the value of i/^ given by the PoiseuiUe-Meyer formula, by inserting in it the given constants of the apparatus and the value of the pressure, time, and volume data observed. Gommendng with Table (949) Iii^tf°«* 296 MEASUREMENT OP HIGH TEMPEBATUBES. [bull. 51 96, which contains data for the smallest radius occurring in the present work, i2=0.0079*^", it appears that the value of //o increases very per- ceptibly as P— i> increases. The different lines drawn correspond to differences in bore of the readjusted tubes. At 9.80o, owing to the length of time of a single observation, only one datum is at hand. Turning thence to Table 97, which holds for tubes of a larger bore (jB=0.0184*'°), the values 1J4 710a . . . are found to lie on very nearly straight lines, which, in comparison with those of the preceding table, have increased enormously in obliqueness ; 7 therefore increases at a rapid rate with P—Pj which rate, however, diminishes as temperature increases, and is nearly zero at 1025^. Now, inasmuch as the rate of axial transpiration decreases with temperature, and inasmuch as Meyer's formula fails for values of the velocity of the particles above a certain datum, these curves suggest that the observed decrement of slope of the lines produced by temperature is due to the decrease of the axial velocity of the transpiring particles produced by the same cause. In this place the differential results of Table 103 are available, and furnish data for 77625- The values for 77975, which Table 103 also con- tains, are, in general, in good accordance with the data of Table 97, and are therefore not essential to the diagram. Tables 98, 99, and 100 contain results for the largest value of radius, 22=0.027*'™, occurring in these experiments. In Table 98 the results 775, 7i4i Viooj show a tendency to curvilinear loci. But the true character of the phenomenon appears none the less clearly. The mean rate of increase of 77 with P—p is distinctly larger than in the previous instance (Table 97). Again the slope decreases as temperature increases, and is practically zero at 930o. Here, therefore, the effect of the axial velocity of the transpiring particles is again apparent. Table 99 is more full as regards the sequence of data contained, as well as more accurate ; 774 shows a tendency to curvature, but the points may serviceably be grouped on a straight line ; 77^76 is the mean of the first set of results for tempsratures of the Argand air-bath. Inasmuck as pressures are high and low alternately in both this series and the next, the line connecting corresponding observations has fair claims to accuracy. The data substantiate the inferences drawn with refei^nce. to Table 88. The lines are all oblique and they approach horizontality in proportion as higher. temperatures are reached. I may notice here that in case of high temperatures the cooling effect of air passing through the capillary under high pressure was very dis- tinctly discernible, the thermo-couple showing differences of 20° to 4(P between the maximum and minimum rates of flow. Table 100 finally contains results of my largest radius, jB>0.027«"», the exact value of which I do not now care to measure, because the capillary apparatus has been carefully put together and all mercury manipula- tions involve danger. In this emergency I made the permissible sup- tion that for P— j)=0, the value of 7f^ is the same as that in Tables (950) BABUB.] VISCOSITY OF GASES. 297 97 to 99. This enabled me to reduce my relative data to the same standard as h61ds for the Tables 97 to 90. The diagram obtained fully corroborates all the inferences deduced. The obliquity of the lines decreases from low to high temperatures^ i, e.y in proportion as the velocity of the axis flow decreases. Apparent viscosity and temperature. — Considering these results as a whole, and representing the values of ?/ when P— j?=0 as a function of temperature, d''^ it appears that the curves lie farther away from the law t/'=tfo (l+flt^')* '^ proportion as ii is larger. Thus the results, ;;, of Table 96, iJ=0.008^™, conform very fully with this law; the results of Table 97, ii=0.018*'™, fall considerably below it, and finally the results of Tables 98 to 100 where Rs=i0.025^^ lie in a very pronounced way below the former. As the bore is chosen larger, therefore, the effect of temperature becomes gradually less pronounced, and for iJ=0.025«™ the law falls even as low s^r/'=?^o Vl+a6''. On the other hand, as the bore is chosen smaller the curves ultimately (22=0.008*^™) coalesce with thelaw,;/'=7o(t+«^")*. Obliquity of the linear lod. — In Table 104 1 give a perspicuous view of the observed obliquity of the lines in Fig. 64, p. 304, (p being the angle of these lines with the horizontal relatively expressed. The temperature of transpiration being ^^ the value — in the table is computed from Vo — = (1+a^')*. \-\ however is computed from Fig. 64 when P— .j?=0. Table 104. — Transpiration of air in wide tubes. 0" • 977 4 100 625 1025 4 875 8G5 1000 7 1060 1280 *8 t8 •^1 Ji tan^ V". no InoJ ^ 10* 0.008 (Table 96) 0.018 (Table 97) 1.00 2.79 1.02 1.10 2.14 2.66 1.02 1.81 2.06 2.88 1.03 2.13 2.50 20 (00) 314 298 64 7 461 228 166 30 488 128 44 274 92 124 1.00 2.77 1.02 1.23 2.23 2.84 1.02 2.30 2.60 2.80 1.03 2.88 3.20 240 668 223 244 474 587 226 404 458 631 228 478 560 198 100 245 0.025 (Table 99) 0.026 (Table 100) 0.018 (Table 108) 012 (Table 107) ? \ Air. t Hydrogen. (951) 298 MEASUREMENT OF HIGH TEMPERATURES. [BULUSIb For the given valac of 6=9i^ the valaes of the tan (p decreaae about as rapidly as the square of R. It is to be noticed, however, that the tan (p in the case of Table 96 is probably zero, since the observed posi- tive tan q) in Table 104 is compensated by an observed negative tan tp in other similar cases. Hence if tan

(i. e., the ob- liquity (p) occurs in case of silver tubes, the capillary being employed in two dififerent lengths. Curiously enough, the value of q) here does not vary with L, There may, however, be a compensation in R. Silver capillary tubes could not be obtained in such excellent quality as the platinum tubes. (952) BABOt.] VISCOSITY OP GASES. 299 Tablb KfQ.—Tranapiration in silver tube$. [SflTor capillary tabe No. L i==71.00»-. J2=0.01B1«. V=Sm^. ft^e.?*.! p P t" 0" T o 122.61 75.85 281 34370 6.7 22.7 0.0002612 122.61 75.85 282 34490 6.7 22.7 2620 88.07 76.85 086 2G040 6.7 22.7 1078 87.08 75.85 002 26010 6.7 22.0 1076 87.93 75,85 002 25880 6.7 23.0 1960 122.46 75.85 280 84120 6.7 23.1 2600 [Same spiral shorteoecL Xc=35.27«"*.l 110.50 75.00 158 17220 6.7 22.2 0.0002620 110.56 75.90 154 17310 6.7 22.0 2631 87.86 75.00 520 12820 6.7 21.8 1056 87.44 76.00 521 12040 6.7 21.6 1071 110.46 75w00 155 17380 6.7 21.2 2645 Table 107, with resalts for a fine platinam capi llary, has been iucor porated here, and corroborates the present results. Tablb 107. — Transpiration in platinum tubes. Air, [Capillary tube No. 0. 2;=21.2«. 22=0.0118—. F=^466.7-. »=7.0o.] p P <" £-P. xf" P •" T o •123.66 47.74 531 66640 7.0 10.0 0.0003040 123.80 47.88 630 66740 7.0 10.5 8000 8&17 12.25 2137 56570 7.0 20.1 2601 88.05 12.13 */163 56660 7.0 20.6 2607 83.30 12.88 2112 56540 7.0 21.2 2600 1 123. 63 47.74 625 65000 7.0 22.4 8053 •p = 7« ».02. ft 9^75.80 • Table 108, with which I will close the present series of supplementary data, has a direct and important bearing on the discussion. Hydrogen and air are here passed through the same platinum tube consecutively. (953) 300 MEASUREMENT OP HIGH TEMPERATURES. (BULL 54. Table lOS,-^ Transpiration in platinum tubes. Hydrogen. [Capillary tube No. 8. i=40.5«- JB=0.0182«-. F=565.7««. tf=7.8o. p=74.05«».J p P-P r — ■ '^- -kV' P e" T 112. M 37.69 107 10060 o 7.8 22.6 0.0001354 112. 52 87.55 107 10050 7.8 22.7 1355 112.06 87.00 108 0900 7.8 22.8 1347 85.75 10.78 352 8160 7.8 22.0 1100 85.72 10. 75 354 8160 7.8 23.1 1101 85.64 10.67 355 8120 7.8 23.2 1006 112.72 37.75 107 10110 7.8 23.3 1365 112.67 37.70 107 10000 7.8 23.4 1865 [Same apparatus with air.] 120. 47 45.55 202 24000 7.8 23.4 0.0003240 120.55 45.63 201 23930 7.8 23.6 3335 86.66 11.74 676 17120 7.8 23.2 2311 86.59 11.67 675 16080 7.8 23.0 2202 120.52 45.60 202 24030 7.8 22.8 3238 The results are very instructive. lu the experiments (Fig. 54, p. 304) tan (p increases with the rate of flow, or, cseteris paribus, with the vis- cosity of the gas. Hence one would infer that in the case of hydrogen and air passing through the same tube, ceteris paribus, the obliquity would be decidedly greater. The experiment shows precisely the re- verse result; tan tp diminishes more than x)roportionally to the viscosity the ratio (Table 104) being as 3 : 2. General remarks, — I regret that my research must be closed with these experiments, and that it is not expedient to continue the work further. To do this I should need to repeat the work with special care in the measurement of temperature and in the determination of the ca- pillary radius. Nevertheless, the survey of the present field of inquiry is by no means unsatisfactory. My results show conclusively that the character of the internal surface of the transpiration tube is of marked influence on the result. The absence of obliquity {(p) in glass, and its frequent occurrence in metallic tubes, may be referred to the smooth- ness and roughness of the respective internal surfaces. Kongh surfaces are associated with eddies along the line of flow, by which it is retarded and apparent viscosity is increased. Tlie absolute value of viscosity measured by transpiration through metallic tubes is greater than the viscosity measured by transpiration through glass tubes. This I have in general found, and although the eflect of the discrepancy, possibly due to roughness, is not vital in case of my smallest tube. No. 10 (Tables 81 to 90, i2 = 0.008^™), I have none the less thought it wise to state my result, t/'=tfo (1+^ ^^0^ 9 ^i^^ caution, and to pursue the present critical (954) »ABU8.] VISCOSITY OF GASES. 301 inquiry as far as the present section indicates. Inasmuch as I have proved that as JB decreases from my largest to my smallest radius, the value o^ F{d"), which holds for P— |>=0, increases and finally merges into (1+ ^ ^')^ independently of pressure, I have accomplished the main purposes of this section. Intimately connected with the present discussion is the occurrence of surface condensation of gases on platinum. If the law of inverse squares holds, then there will be no tendency of gases to condense in the capillary canal, however finitely small. This follows from the con- stant potential of a homogeneous elliptical shell (of which the capillary tube may in a special sense be said to be compounded) on any points iuclose Meyer : Kinetische Theorie d. Gase, p. 152. Barus : Wied. Ann., vol. 36, 18ti9, p. 383. BABUB.) VISCOSITY OF GASES. 303 ▼olving changes of the capillary bore of the tabes, no fixed or elaborate form of transpiration pyrometer would have served* as well as the im- provised arrangement described in Figs. 45 and 46. Equation 12, how- ever, contains the clue for the construction of a practical transpiration pyrometer. The equation shows that the correction for ends decreases with extreme rapidity with the ratio of bores of the cold and hot parts of the pyrometer, i. e., as the fourth power of E'^o/Rq. Hence the dis- torting effect of cold ends can be easily eliminated by making the cen. tral parts of the tube slightly more capillary than the terminal parts. The accompanying diagrams suggest some serviceable methods by which this may be done. Fig. 49 represents an available form of apparatus in which the termi- nal tubes a and h are relatively large, each of semicircular section with their flat sides juxtaposed. The capillary tube is shown at c Cy and may be wound in any desirable spiral form, open or closed. To protect it an envelope d of platinum surrounds the helix of capillary tube o o., With regard to this form, it is to be noticed that the interior volume in the terminal tubes a and b must be reduced as far as possible so that thermal changes of the air inclosed may not sensibly affect the result. In view of the difficulty of welding the capillary tube c o into the larger terminal a and &, the form Fig. 50 has advantages. Here the terminal a is a circular tube, and is drawn down upon the capillary tube e by aid of the wire plate. By this method a tight joint may be produced in such a way as not to endanger the platinum capillary. Slight changes of the » ^-JUCSUUUULSULSb ) FIO.49. -t FlO.80. mtmmmmr r VE0.6L T ^a^ Fxo. 53. FiOB. 40, 60, 51, 62, 53, Plagrams of praotioal traaplratlon pyrometscv (951) MEASUREMENT OF HIQU TEHPEBATUBES. [bull. 51. capillarj bore for thetmall length d, where the two tubes are in con- tact, will only change the mean radiae R,, and will be falty al- lowed for in measoring— in the manner indicated. (See p. 282.) Another way of making capil- lary tubes with large termiusl ends is shown in the exaggerated diagrams Figs. 61 and 62. In Fig. 51 a smaller capillary tube is inserted at c in the larger tube a b. The latter is then drawn down iu the wire plate nntil e has the requisite small diameter. Again, a simple platinum wire a may be inserted into the tube a b, ua Fig. 5^ suggests. These forms haretheadvautageascouststinK of uniform tubes withont solder- ing, so that the danger of leaks where the terminals join the tube is obviated. Finally, thesimplestandsurest method of decreasing the central capillary bore consists in rolling down the central part in a wire- rolling mill, the two rollers of snch a mill being appropriately grooved, Without passing jndgment on any of these forms, It is clear that the simple capillary tube used iu the above experiments can bo made to subserve the par- poses of thermal raeasarement in the way shown in Fig. 63. Here the ends c' ead si>ace, correction for, 257. Debray studies dissociation of marble, 38. (See Deville.) Decharme, radiation measurements of, 44. Density of platinum alloys, 128, 143, 145. Desbordes, expansion pyrometer of, 26. Deville and Debray study properties of plati- num alloys, 49. Deville and Troost, metallic vapor baths of. 10, 23,24. vapor density bulbs of, 29. final pyrometric work of, 31, 33, 34, 35, 36. condemn non-spherical bulbs, 48. vapor baths of, 56, 57. large apparatus of, 84. select spherical bulbs, 174. compensator devised by, 192. zinc, boiling point of. 235. Dewarand Gladstone, photometric pyrometry of, 45. Die for porcelain tubes and stems, 06. Differential transpirometer, 210. apparatus for transpiration work, 249. transpiration measurement. 2<.i3. Diffujaiion of guses through platinum. 275. Digest of electrics of platinum alloys, 14.3. of constant pressure air thermometer reaulta, 227. INDEX. 301) Dilatation of solids, 25. of gases, 27. of liquids, 27. Dimensions of capillary tubes, 171. Disintegration of platinum at high temperatures, 276. Diq>laoement methods of air thermometry, 36. air thermometer, 165. Disposition of air thermometrio apparatus, 187. Dissociation of iodine, 24. pyrometry,38. effect of, on viscosity, 279. transpiration method for, 306. Dixon graphite, crucible of, 73. Draper, law of radiation of, 43, 46. Dumas, vapor density method of, 29. Duration of continuous ebullition, 116, 118. E. Ebullition, use of, in pyrometry, 42. plane of, 1U8. continuous, duration of, 116, 118. Elasticity, phenomena of. 17. Electrical conductivity, pyrometers based on, 50. Electric phenomena in furnace, 233, 231. RUicot, dilatation thermometer of, 25. Elliott, standard cell of, 100. Bister and Geitel on disintegration of platinum, 276. Erhardt and Schertel measure melting points of alloys, 34. fusion experiments of, 40. Erhardt, calorimetric work of, 42. Erhardt and Schertel test Jolly's air thermome- ter, 208. Ermann and Herster, air thermometer of, 28. Errors of constant volume air thermometer formuhc, 190, 196. simplified formulfe,214. of viscosity measurements, 274. v.Ettinghausen measures temperature coefficient of I^itimer Clark's cell, 102. Expansion of solids, 26. of gases at high temperatures, 37. Exponential law, advantages of, in pyrometry. 277. P. Fiducial reading of air thermometer, 186. Fievez, photometric pyrometry of, 46.. Fire clay classified by viscosity measurements, 46. air thermometer. 20,64,237. Fischer, pyrometric work of, 23. calorimetric pyrometer of, 41. criticises Siemens' pyrometer, 51. Fletcher combustion furnace, 166. Forms of transpiration pyrometer, 303. Formula of A venarius, insufficiency of, 125. Formulae), thermo-electric, how used, 103. forconstantvolumeair thermometer, 188, 190. for air thermometer, errors of, 190. Formulae for constant pressure air thermometer, 210. 0implified,211. Formulse, errors of simplified forms of, 214. for experimental errors in constant pressure air thermometry, 227. for thermal changes of viscosity compared, 277. for transpiration pyrometry, 281. for wide transpiration tubes, 285. Forster criticizes Siemens's pyrometer, 61. Frontispiece described, 187. Puess, metallic air thermometer of, 33. Furnace for boiling zinc, 64. for small boiling crucible, 92. for revolving muffle, 180. 188. Fusing points measured by Violle, 39. Fusion, phenomena of, 17. pyrometers, 39. of wires of thermoKX>uples, effect of, 94. of alloys, 128. G. Gaseity, effect of imperfect, 279. Cjas expansions, comparison of, 238. Gases, expansion of, 27. high-temperature expansion of, 37. electrical resistance of, 52. condense on solids, 301. Gasometers, 179. Gauntlet, expansion pyrometer of, 26. Gibbon, expansion pyrometer of, 26. Gibbs's ring-burner, 85, 89, 90. Glass re-entrant air thermometer, 237. Gleitungs coefficient, 276,302. Helmholz on, 251,252. Gooch, suggests ring-burner, 85. sodium tungstate luting of, 93. Gosse, apparatus of, 21,31. Govi, radiation pyrometer of, 43. on transparency of metals, 164. Graham, transpiration work of, 47. on gas transpiration, 241, 241. Graphite crucible, large form, for zinc, 73. Grassi, studies dilitation of gases, 33. Gray and Trannin, photometer of, 44. Greiner, Emil, apparatus of, 21. boiling tubes of, 89. Groshans, principle of, 22. Grunow, William, apparatus of, 21. air-thermometer stand of, 167. cathetometer of. 251. Guthrie, on efflux through short tubes, 242. Guy ton-Morveau, calorimetric pyrometer of, 40. pyrometric work of, 25, 26, 28. H. Hagen, transpiration data of. 241. Hall'& Sons, apparatus of, 21. Ilallock, Dr. William, appointment of, 18. work done by. 19, 20. constructs furnace for zinc, 62. suggests arch for insulator machine, 96. tests displacement thermometer, 165. modifies the Jolly-Pfaundler stand, 167. air-thermometer measurements of, 200l {See Chapter I.) Heat conduction, phenomena of, 17. pyrometry based on, 42. 310 INDEX. Heat expansion of porcelain, 236. Heating, rates of, in muffle furnace, 203, 201. method of, for transpiration work, 249. Heeren, fusion pyrometer of, 39. Helmholtz on Gleitung's coefficient, 252, 276, 302. Helix of platinum capillary tubing^, 244,800. of capillary tube, how wound, 248. of capillary tube, early form of, 258. later form of, 267. High temperature measurement, difficultit^ of, 24. data, accuracy of, 54. Historical account of methods of pyrometry, 24. Hoadley, calorlmetric pyrometer of, 42. Hobson, calorlmetric p3n*ometer of, 41. Hoftnann, on efflux through short tubes, 242. Hoflfknann*8 formula) for wide transpiration tubes, 286. Holden, Dr. Austin, aids research, 19. Holman, Silas W., on viscosity of gases, 210,241, 242. formula of, for viscosity and temperature, 279,280. Holman, transpiration, method of, 3C2. Hydrogen permeates platinum, 261, 275, 283. I. Illustrations, table of, 9, 10. In-glaa:ed porcelain bulbs, 174. Insulators, machine for making. 95. Interpolation methods of pyrometry, 52, 54. Iodine vapor, pyrometrlc use of, 24. 29. Isambert, studies dissociation of solids, 38. J. Jenkin, F., tabid of specific resistance of, 157. Jet pumps of Professor Richards, 242. Jolly, air thermometer of, 32. form of air thermometer of, 1G7. Jourdes, heat conduction pyrometry of, 42. K. Kasrser on condensation of gases by solids, 301. on disintegration of platinum, 276. Kinetic inferences fur viscosity of gases, 273. King, Clarence, suggests researches, 17. instructions of, 17. KJttler measures temperature coefflcientof I^iti- mer Clark's cell, 102. Knott, MacQregor, and Smith, thermo-elcctrics ofcobaltof,49. thermo-electrics of platinum alloys of, 49. Kovesligethy, radiation work of, 46. Kohlrausoh and Ammann, sero method of, 97. Kundt, capillary glass connectors of, 171. Kundt and Warburg, apparatus of, for viscos- ity, 241. L. Lamy, dissociation pyrometer of, 38. Landolt and Boemstein*s tables, 40, 42. use of, 213. lAnger. {Sre Meyer.) Langley, bolomctric work of, 44, 46. lAtimer Clark's standard cell, 97, 99, 102. I^uth, pjrrometrio work of, 23. studies fusion of silicious mixtures, 40. circulating water pyrometer, 43. Law of fifth powers of Maxwell, 277. Le Chatelier, high temperature work of, 22. fusion experiments of, 40, 50. thermo-electric work of, 49. platinum-rhodium couple of, 50. pyrometric work of, 84. Limit of thermo-electric thermosoopee, 53. Limit thermo-couples, 81, 83. Lion and Guichard, expansion pyrometer of, 27. Liquids, dilitation of. 27. List of th^rmo-oouplee, 68. M. MacGregor. {See Knott.) MacGrcgor and Knott, resistance of iridioplatl- num.Sl. Machine for making insulators, 9C. Machine for soldering porcelain, 175. Magnus, measures expansion of gases, 33. Magnetism, pyrometers based on, 52. Main, heat conduction p3rrometry of, 42. Malvern Platinum Works, apparatus of, 21. Manipulation of revolving muffle, 185. Manometer for air thermometry, 167, 188. Matthiessen, resistance measurements of. 26. Matthiessen and Vogt, electrics of alloys of, 157. Mariotte flask, how improved, 244. Maxwell, viscosity of gases studied by, 46. law of gaseous viscosity, 240, 241, 252. Maxwell on viscosity and temperature, 277. on mean free iMith, 274. Mayer, A., acoustic pyrometer of, 47. Mean free path introduced by Clausius, 240. relations of, to temperature, 274. Mercury, vapor bath of, data for large, 69. constant temperature of, 106. small form of vapor bath for, 84. Metallic boiling points, 29, 30. Metals, specific heat of, by Yiolle, 41. all dissolved by platinum, 127. Methods for viscosity measurement, 247. Meyer, O. E., transpiration formula of, 47. on viscosity and transpiration of gases, 240, 241. derives transpiration formula of gases, 251. on the sliding coefficient, 276. on viscosity and temperature, 277. temperature coefficient of viscosity of, 279. Meyer, Victor, pyrochemic work of, 25, 34. dissociation of iodine, etc., 30. vapor density method of, 36, 37. Meyer, calorimctric work of, 42. Meyer, Victor, suggests boiling-point substan- ces, 121. pyrochemical researches of, 37. on expansion of gases, 248. Mill, air thermometer of, 28. Miller, calorimetric pyrometer of, 41. Moisture in unglaised bulbs, 198. Morlent F'rt^rcs, porcelain work of. 21. McSwceney, radiation pyrometer of, 48. INDEX. 311 MafBe furnace, rates of heailngr and coolinff, 308, 201. Muffle, revolving. 180, 183. Miiller measure* resistance at higrh tempera- tures, 50. Multiple arc, thermo-electric eflPect of, 82. Muflschenbroeck, dilatation thermometer of, 25. N. Nahrwold on disintegration of platinum, 276. Natanson on molecular airgreKation, 280. Navier on efflux from apertures, 242. on transpiration in short tubes, 285, 289. New Haven, (>>nn., laboratory work at, 18. Newton, Sir Isaac! radiation pyrometry of, 43. Nichols, pyromet^c work of, 23, 26. Nichols, E. L., radiation pyrometry of, 44. on expansion of platinum, 47. criticises resistance pyrometers, 51. Nomenclature used In viscosity, 256. O. Obermayer, thermo-electric work of, 50. on transpiration of gases, 241. temperature coefficient of viscosity of, 279, 280. Oechsle, expansion pyrometer of, 26. Oxide coats on steel, 46. Oxybydrogen blowpipe, 177. P. Peclet, heat conduction pyrometry of, 43. Pelouze, treatise of, on pyrometry, 23. J^erkiu, resistance of gases at high tempera- tures, 52. Pemolct, siliciflcation of platinum, 187. Person, mercury pyrometer of, 27. Petersen, expansion pyrometer of, 26. air thermometer of, 28. Pfaundler, air thermometer stand of, 167. Photometric pyrometry, 43, 45. Pionchon, on specific heat of iron, 41. Plane of condensation, 108. of ebullition, 108. Platinum couples with vanishing amounts of impurity, 57. iridium couple, anomalies of, 115. thermo-electric datum ftir uielting-point, 124. purified by heating, 126, 146. siliciflcation of, 187. pervious to hydrogen, 264, 275, 283. disintegrates at high temperatures, 276. Plattner, fusion experiments of, 3U. Poifleuille, law of transpiration of, 241. Poiseuille-Meyer, transpiration formulae, 210, 242, 251. law not applicable, 284. Poison on transpiration in short tubes, 285. Porcelain, stem sagged into bulb, 22. air thermometer, standard form of, 22. coefficient of expansion of, 29. air thermometer, 31. expansion of, 31, 35, 36, 236. air thermometer bul bs, 1 7 1 . machine for soldering, 175. Pouillet, pyrometric work of, 28. air thermometer of, 28. calorimetric pyrometry studied by, 41. thermo-electric pyrometry of, 48. Practical calibration, data for, 110. Pressure, effect of, 6n thermo-couples, 53. apparatus for transpiration work, 244. eflfect of, on transpiration in wide tubes, 2S6. Prinsep, pyrometric work of, 26. standard air thermometer of, 28. Aision pjrrometer of, 39. Prinscp's alloys for fusion work, 84,90. Problems to be undertaken, 17. De la Provoetaye, radiation pyrometry dlsonmnd by, 44. Prussian porcelain works, apparatus of, 21. Puluj on viscosity and teni|)eratiire, 241. temperature coeffldeut of visooaity of, 279, 280. Purity of platinum, 146. Pyrognomic substances, 46. Pyrometer based on circulating water, 43. transpiration, forms of, 303. Pyrometers, classification of, 25. of fusible alloys, 39. limit of thermo-electric, 53. based on specific heat, 40. ebullition, 12. viscosity, 46. acoustics, 47. thcrmo-electrics, 48. electrical conductivity, 50. Pyrometry, advantages of thermo-electric, 52. interpolation methods in, 52. new viscous method of, computation for, 281. rcHultH for tmnspiration, 282. transpiration method of, practical remarks on, 302. Pyrometry based on heat conduction, 42. radiation, 43. Q. Quincke devises resistance pyrometer, 51. R. Radiation pyrometry, 28, 29. 43. liudius of capillary tubes, 257. how measured, 289. obtained by transpiration, 282. transpiration, measurement of, 255. Ramsay on trauHparency of metals, 164. Rayleigh, measures temperature coefficient of l4itimer Clark's cell, 102. Reductions, tliermo-electric, 67, 77. Ko-entrant porcelain bulbs, 173. Reguault, standard air thermometer of, 28, 31, 167, 248. measures expansion of gases, 33. displacement pyrometer of, 36. thermo-electric pyrometer of, 48. capillary tul)es, 1G7, 169. Reissig, resistance pyrometer of, 51. Resisluncc, electrical, pyrometers bas49d on,o0. of platinum alloys, 115, 133. Resistonietcr, 131. Reynolds, Osborne, on elllux through short tul)es, 242. Richards, jet pumi»s of, 242. 312 INDEX. Rieinsdyk, fusion pyrometer of, 39. Ring burner of Dr. Gibb«, 85, 89, 90. KulMsrts, fusion experiments of, 39. KoMctli on solar temperature, 45. liounia tests Wallaston*s method, 170. I^everberatory furnace for zinc, 64. Bevolvins muffle furnace, 180. advantaeres of, 185. 8. Saintignon, circulating water pyrometer, 43. Si^otBchewsky, vapor tension studied by, 38. Salleron, calorimetric pyrometer of, 41. SalU, specific heat of, by Ehrhardt, 42. Saxon porcelain works, apparatus of, 21. ^ Scala graduum caloris, 43. Schinz, calorimetric pyrometer of, 41. pyrometrio work of, 32, 33. displacement pyrometry of, 36. heat condaction pyrometry of, 42, 43. thermo-electric pyrometry of, 48. re-entrant air thermometier of, 48. Schinz^s torsion galvanometer, 104. Schlelermacher tests Stefan's law of radiation, 44. resistance pyrometry of, 51. Sohneebeli tests Stefan's law of radiation, 44. Schneider, calorimetric table of, 41. Schubarth, calorimetric pyrometer of, 41. Schumann on transpiration of gases, 241. on condensation of gases by solids, 301. Schwarz, calorimetric pyrometer of, 40. Seochi on transparency of metals, 164. Seger studies fusion of siliceous mixtures, 40. Selenium, boiling point of, 34. Series of thermo-couples, 57. of alloys, 79. Shaw, pyrometers classified by, 28, 27. vapor tension studied by, 38. Siemens, resistance measurements of, 26. calorimetric researches of, 41. Siemens*s pyrometer, 33, 51. Silbermann and Jacquelln.air thermometer of, 28. Siliceous mixtures for fusion work, 40. Silicification of platinum, 187. Siphon Daniell,99. Sliding coefficient, 276,302. SoUir temperatures, 45. Soldering of porcelain , 31, 175. Solids, dilatation of, 25. Solly, thermo-electric pyrometer of, 48. Soret, temperature of the sun measured by, 45. Specific heat, pyrometers based on, 40. Sprengel pump used by Deville and Troost, 34. Spring on wire drawing, 170. Springmuhl on transpiration of gases, 241. Standard cells, temperature coefficient of. , 102. Standardization by comparison, 22, 237. of constant pressureair thermometer, 212. Stas photometric pyrometry discussed by, 46. Steam, superheated, used in displacement ther- mometer. 166. Steftin, law of radiation of, 44. transpiration work of, 47. flow of viscous liquids, 241. pn transpiration in short tubes, 285. V. Steinle and Ilartung, graphite nvrometcrof. it. Stenger, radiation work of, 46. Stokes on viscosity* of air, 24U. flow of viscous liquids, 241. on transpiration in sliurt tuben, 285. Strouhal, Vincent, aids research, 17, 18. electrics of steel, 144, 149, 159. improved thermo-electric appRratu» of, 97, 9S. de St. Venant on transpiration in short tubes, 285. Substances for boiling points, 119. Summary of results for large vapor baths, 79. Sulphur, small form of vapor bath for.H5. vapor bath, constant temperature of. 107. Sun, temperature of, 45. T. Table for (l+i{^()/(l+a0,212. of errors in constant pressure air thermom- etry, 229. Tables, list of, 11, 12, 13. Tait, thermo-electric researches of, 49. silicification of platinum, 187. Temperature, how computed thermo-electri- cally,71. coefficient, how measured, data, 139. coefficient of standard cells, Ui2. coefficient and resistance, r-7. coefficient, zero value of, 161. effect of, on wide tube transpirations, 297. Temperatures, constancy of, in IniilinK tul>es. 104. equality of, tested thermo-electrically, 67. Tenacity of thermo-couplcji, 53. Thermal conductivity, pyrometers based on, 42. rniermo-couples, list of, 68. Thermo-couple of platinum and platinum, 81. Thermo-electric pyrometry, advantages of, 52. pyrometers, 48. anomalies, tests for, HO. computation, 103. work, galvanometer measurement, 104. calibration, practical data for, 110. constants, time variations of, 116. datum for fused platinum, 124. equation, insufficiency of. 125. Thermo-electrics of platinum alloys, 135. Therm oecopes, classified by Thomson, 25. magnetic, 52. Thermostat and transpiration pyrometer, 305. Thomson, James, equation of, 22. Thomson, J. J., resistance pyrometry of, 52. Thomson, Sir William, article " Heat" of, 23, 25. classifies pyrometers, 25. vapor tension thermometer of, 38. viscosity pyrometer of, 46. thermo-electric diagram of, 49. magnetic thermoscope of, 52. Tidblom, thermo-electric formulep of, 50. Time variations of thermo-electric constAnts, 116. Tin, boiling point, experiments on, 123. Torsion g^olvanometer for high temperature measurement, 22. for thermo-electric work, 104. Transparency of metals, 161, INDEX. 313 Transpiration apparatus described, 212, 244. manipulation of. 255. Transpiration data vitiated by condensation of gas, 301. devic-es for rapid, at high temperatures, 2H4. diflTerential measurement of, 293. during long intervals. 293. Transpiration formultp, conditions of, 252. for two cold ends, 252. for difTerential apparatus and cold ends, 254. Transpiration in wide tubes, data for, 287, 288. effect of pressure on, in wide tubes, 295. in wide tubes influenced by temperature, 297. in wide tubes, general remarks on, 300. in glass tubes, 298. in silver tubes, 290. in platinum tubes, 3G0. measurement of capillary radii, 256. not subject to Poiseuille-Meyer*s law, 284. Transpiration pyrometry, oapillary apparatus for, 245. form u lie for, 281. advantages of, 281. results for, 282. practical remarks on, 302. forms of, 303. protection of, 306. Transpiration under variable pressure, 287. Troost, studies dissociation of iodine. 30. measures boiling ixiint of selenium, 34, 35. diff'usion pyrometer, 39. boils selenium in glass, 80. boiling point of selenium, 121. on expansion of gases, 248. T ubes, aipi 1 lary , of m etal , 1 69. Turner on transparency of metals, IfVl. V. Vacuum boiling points of metals, 95. Vapor bath, mercury, data for large, 69. of zinc, data for large, 70. Vapor bath, small form of, for low tempera* tares, 84. for mercury, 84. for sulphur, 85. forms of, for high temperatures, 90. Vapor bath, of mercury, constant temperature of, 105. of sulphur, constant temperature of, 107. of zinc, constant temperature of, 108. Vui>or baths, liquids for, 119. VaiK>r tension pyrometry, 38- Velocity of the mean square, 274. Violle, py rometric work of, 21, 49. measures boiling point of zinc, 35. fusion experiments of, 39. important calorimetrio work of, 41. radiation pyrometry of, 44. temperature of the sun estimated by, 45. siliciiication of platinum, 187. zinc, boiling point of, 235. Viscosity, phenomena of, 17. of Are clays, 40. of platinum at high temperatures, 293. Viscosity of gases, pyromctrio uso of, 46,248. measurement, methods of, 247. datA for, 258. values of, at zero degrees, 271. kinetic inferences, 274. advantages of an exponential law in, 277. Viscosity measurement, errors of, 274, 275. temperature coefficient of, 279, 280. Vogrt. {See Matthiessen.) Volatilization, experiments on, 121. Volume tube, graded for air thermometer, 210. Volumetry of compensator canal, 193. of bulbs for air thermometer, 213. W. Warburg on transpiration of gases, 241. temperature coefficient of viscosity of, 279, 280. Water attacks glass at high pressures and tem- peratures, 27. Water jacket for volumeter, 210. Waterston, measures high temperature expan- sion of water, 27. , Weber, H. F., radiation work of, 46. Weber, L., electrics of alloys measured by, 145. Wedgwood, pyrometer of, 25. Weinhold, pyrometric work of, 23, 24, 26, 32, 33. on dissociation pyrometry, 39. calorimctric work of, 41. studies rcsLstance pyrometer, 51. tries Jolly's air thermometer, 208. zinc, lM}iling point of, 235. WhitAll, Tatum & Co., apparatus of, 21. Wiedemann, E.,on transpiration ofgases, 241, 242. temperature coefficient of viscosity of, 2H0. Williamson criticises Siemens* pyrometer, 51. Wilson, calorimctric pyrometer of, 41. Winkler on the graphite pyrometer, 27. Wires, platinum, mechanical treatment of, 128, 133. Wirkungssphiire, 274. Z. Zabel, air thermometer of, 32. Zero of temperaiure eoeffleicnt, 161. Zinc, boiling point of, 2 1, 29, 30, 31,^1,35. boiling point, furnace for, 62. largo vapor b:ith of, data for, 70. large crucible for, 73. vapor bath, eonsUint temperature of, 108. . coincidence of l)oiling point, data for, 115. vapor, calibration in, 122, 123. boiling point of, measured, 233,235. ■ I 1- II ii I!' ii ■f I i n ^ i 3 blDS D22 S5fl fibfi i 1. • •. t-